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A General Inequality for CR-Warped Products in Generalized Sasakian Space Form and Its Applications Open
In the present paper, by considering the Gauss equation in place of the Codazzi equation, we derive new optimal inequality for the second fundamental form of CR-warped product submanifolds into a generalized Sasakian space form. Moreover, …
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Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms Open
In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds o…
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Characteristics of space network system formed by the constituent elements in urban streets: Tianzifang in Shanghai as a case study Open
Using a street in Shanghai as a case study, a strategy was developed to study an urban network space system by analyzing and interpreting street space from the microscopic perspective of urban composition elements. At the methodological le…
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Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms Open
This study establishes new upper bounds for the mean curvature and constant sectional curvature on Riemannian manifolds for the first positive eigenvalue of the q-Laplacian. In particular, various estimates are provided for the first eigen…
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On a type of almost Kenmotsu manifolds with harmonic curvature tensors Open
Let $M^{2n+1}$ be an almost Kenmotsu manifold with the\ncharacteristic vector field belonging to the $(k,\\mu)'$-nullity\ndistribution. We prove that the curvature tensor of $M^{2n+1}$ is\nharmonic if and only if $M^{2n+1}$ is locally isom…
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Research on space optimization of historic blocks on Jiangnan from the perspective of place construction Open
In the process of rapid urbanization, gentrification and commercialization have inevitably appeared in the historical districts of Jiangnan. Although they optimize the space environment of the historic district and promote the development …
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NOTES ON REAL HYPERSURFACES IN A COMPLEX SPACE FORM Open
We characterize a homogeneous real hypersurface of type (A) or a ruled real hypersurface in a non-flat complex space form, respectively.
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On the characterizations of f-biharmonic legendre curves in Sasakian space forms Open
We consider f-biharmonic Legendre curves in Sasakian space forms. We find curvature characterizations of these types of curves in four cases.
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On Differential Equations Characterizing Legendrian Submanifolds of Sasakian Space Forms Open
In this paper, we give an estimate of the first eigenvalue of the Laplace operator on minimally immersed Legendrian submanifold N n in Sasakian space forms N ˜ 2 n + 1 ( ϵ ) . We prove that a minimal Legendrian submanifolds in a Sasakian s…
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ON SOME GEOMETRIC PROPERTIES OF QUADRIC SURFACES IN EUCLIDEAN SPACE Open
This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second me…
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Twisted surfaces with vanishing curvature in Galilean 3-space Open
In this work, we define twisted surfaces in Galilean 3-space. In order to construct these surfaces, a planar curve is subjected to two simultaneous rotations, possibly with different rotation speeds. The existence of Euclidean rotations an…
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A Comparative Study on the Spatial Layout of Hui-Style and Wu-Style Traditional Dwellings and Their Culture Based on Space Syntax Open
Hui-style and Wu-style traditional dwellings adopt different connection modes, reflecting different spatial characteristics and resulting in different spatial layout characteristics. The rationale for this is related to the differences bet…
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Differential Geometry of Submanifolds in Complex Space Forms Involving δ-Invariants Open
One of the fundamental problems in the theory of submanifolds is to establish optimal relationships between intrinsic and extrinsic invariants for submanifolds. In order to establish such relations, the first author introduced in the 1990s…
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Chen–Ricci Inequality for Isotropic Submanifolds in Locally Metallic Product Space Forms Open
In this article, we study isotropic submanifolds in locally metallic product space forms. Firstly, we establish the Chen–Ricci inequality for such submanifolds and determine the conditions under which the inequality becomes equality. Addit…
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The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms Open
In this work, we first derive a generalized Wintgen type inequality for a Lagrangian submanifold in a generalized complex space form. Further, we extend this inequality to the case of bi-slant submanifolds in generalized complex and genera…
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On parallel ruled surfaces in Galilean space Open
In this paper, we investigate the parallel surfaces of the ruled surfaces in Galilean space. There are three types of ruled surfaces in Galilean space. We derive the necessary conditions for each type of the ruled surfaces of the parallel …
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Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms Open
The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manif…
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Quantitative volume space form rigidity under lower Ricci curvature bound II Open
This is the second paper of two in a series under the same title; both study the quantitative volume space form rigidity conjecture: a closed $n$-manifold of Ricci curvature at least $(n-1)H$, $H=\pm 1$ or $0$ is diffeomorphic to an $H$-sp…
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Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form Open
We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, $\theta $-slant, invariant and anti-invariant submanifolds tangent to…
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Interior-exterior connection in architectural design based on the incorporation of spatial in between layers. Study of four architectural projects Open
Different spatial layers in the architectural structure of a building can create particular spatial relations and an architectural space that cannot be defined as an inner space or as an outer space, but one which has the characteristics o…
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Some Curvature Properties on Lorentzian Generalized Sasakian-Space-Forms Open
In this paper, we investigate the Lorentzian generalized Sasakian-space-form. We give the necessary and sufficient conditions for the Lorentzian generalized Sasakian-space-form to be projectively flat, conformally flat, conharmonically fla…
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Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons Open
The purpose of this article is to obtain geometric conditions in terms of gradient Ricci curvature, both necessary and sufficient, for a warped product semi-slant in a Kenmotsu space form, to be either CR-warped product or simply a Riemann…
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Bounds for generalized normalized δ-Casorati curvatures for Bi-slant submanifolds in T-space forms Open
In this paper, we prove the inequality between the generalized normalized ?-Casorati curvatures and the normalized scalar curvature for the bi-slant submanifolds in T-space forms and consider the equality case of the inequality. We also de…
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Rigidity of linear Weingarten hypersurfaces in locally symmetric manifolds Open
Our purpose in this paper is to study the rigidity of complete linear Weingarten hypersurfaces immersed in a locally symmetric manifold obeying some standard curvature conditions (in particular, in a Riemannian space with constant sectiona…
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Chen optimal inequalities of CR-warped products of generalized Sasakian space form Open
Our main objective of this paper is to derive the relationship between the main extrinsic invariant, and the contact CR δ-invariant (new intrinsic invariant) on a generic submanifold in trans-Sasakian generalized Sasakian space forms. Furt…
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Optimal Inequalities for Submanifolds in Trans-Sasakian Manifolds Endowed with a Semi-Symmetric Metric Connection Open
In this paper, we improve the Chen first inequality for special contact slant submanifolds and Legendrian submanifolds, respectively, in (α,β) trans-Sasakian generalized Sasakian space forms endowed with a semi-symmetric metric connection.
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GAUSS MAPS OF RULED SUBMANIFOLDS AND APPLICATIONS I Open
As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this pap…
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On the existence of closed biconservative surfaces in space forms Open
Biconservative surfaces of Riemannian 3-space forms $N^3(\\rho)$, are either\nconstant mean curvature (CMC) surfaces or rotational linear Weingarten surfaces\nverifying the relation $3\\kappa_1+\\kappa_2=0$ between their principal\ncurvatu…
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On the geometry of nearly trans-Sasakian manifolds Open
The geometry of nearly trans-Sasakian manifolds is researched in this paper. The complete group of structural equations and the components of the Lee vector on the space of the associated $G$-structure are obtained for such manifolds. Cond…
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δ(2,2)-Invariant for Lagrangian Submanifolds in Quaternionic Space Forms Open
In the geometry of submanifolds, Chen inequalities represent one of the most important tool to find relationships between intrinsic and extrinsic invariants; the aim is to find sharp such inequalities. In this paper we establish an optimal…