scholarly journals Constancy of -Holomorphic Sectional Curvature for an Indefinite Generalized -Space Form

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Jae Won Lee
Keyword(s):  
Sectional Curvature ◽  
Space Form ◽  
Sasakian Manifold ◽  
Algebraic Characterization ◽  
Holomorphic Sectional Curvature ◽  
Space Forms

Bonome et al., 1997, provided an algebraic characterization for an indefinite Sasakian manifold to reduce to a space of constant -holomorphic sectional curvature. In this present paper, we generalize the same characterization for indefinite -space forms.

scholarly journals Strongly pseudo-convex CR space forms

2019 ◽  
Vol 6 (1) ◽  
pp. 279-293 ◽  
Author(s):  
Jong Taek Cho
Keyword(s):  
Sectional Curvature ◽  
Hyperbolic Space ◽  
Space Form ◽  
Contact Manifold ◽  
Holomorphic Sectional Curvature ◽  
Sphere Bundle ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Pseudo Convex ◽  
Unit Tangent Sphere Bundle

AbstractFor a contact manifold, we study a strongly pseudo-convex CR space form with constant holomorphic sectional curvature for the Tanaka-Webster connection. We prove that a strongly pseudo-convex CR space form M is weakly locally pseudo-Hermitian symmetric if and only if (i) dim M = 3, (ii) M is a Sasakian space form, or (iii) M is locally isometric to the unit tangent sphere bundle T1(𝔿n+1) of a hyperbolic space 𝔿n+1 of constant curvature −1.

scholarly journals PSEUDO-PARALLEL KAEHLERIAN SUBMANIFOLDS IN COMPLEX SPACE FORMS

2020 ◽  
pp. 321
Author(s):  
Ahmet Yildiz
Keyword(s):  
Sectional Curvature ◽  
Fundamental Form ◽  
Complex Space ◽  
Space Form ◽  
Dimensional Space ◽  
Second Fundamental Form ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Totally Geodesic ◽  
Complex Space Forms

Let $\tilde{M}^{m}(c)$ be a complex $m$-dimensional space form of holomorphic sectional curvature $c$ and $M^{n}$ be a complex $n$-dimensional Kaehlerian submanifold of $\tilde{M}^{m}(c).$ We prove that if $M^{n}$ is pseudo-parallel and $Ln-\frac{1}{2}(n+2)c\geqslant 0$ then $M$ $^{n}$ is totally geodesic. Also, we study Kaehlerian submanifolds of complex space form with recurrent second fundamental form.

scholarly journals Parallel submanifolds of complex space forms I

1983 ◽  
Vol 90 ◽  
pp. 85-117 ◽  
Author(s):  
Hiroo Naitoh
Keyword(s):  
Symmetric Space ◽  
Sectional Curvature ◽  
Complex Space ◽  
Space Form ◽  
Real Space ◽  
Hermitian Symmetric Space ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Simply Connected ◽  
Complex Space Forms

Complete parallel submanifolds of a real space form of constant sectional curvature k have been completely classified by Ferus [3] when k ≧ 0, and by Takeuchi [19] when k < 0. A complex space form is by definition a 2n-dimensional simply connected Hermitian symmetric space of constant holomorphic sectional curvature c and will be denoted by (c).

scholarly journals Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Dae Ho Jin
Keyword(s):  
Vector Field ◽  
Space Form ◽  
Sasakian Manifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Structure ◽  
Sasakian Space Forms ◽  
Generalized Sasakian Space Form ◽  
Characterization Theorems ◽  
Lightlike Hypersurfaces

We study lightlike hypersurfacesMof an indefinite generalized Sasakian space formM-(f1,f2,f3), with indefinite trans-Sasakian structure of type(α,β), subject to the condition that the structure vector field ofM-is tangent toM. First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type(α,β). Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.

scholarly journals A basic inequality for submanifolds in a cosymplectic space form

2003 ◽  
Vol 2003 (9) ◽  
pp. 539-547 ◽  
Author(s):  
Jeong-Sik Kim ◽  
Jaedong Choi
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Sectional Curvature ◽  
Mean Curvature ◽  
Space Form ◽  
The Other ◽  
Space Forms ◽  
Basic Inequality

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely, its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely, squared mean curvature on the other side. Some applications, including inequalities between the intrinsic invariantδMand the squared mean curvature, are given. The equality cases are also discussed.

On 4-dimensional generalized complex space forms

1999 ◽  
Vol 66 (3) ◽  
pp. 379-387 ◽  
Author(s):  
Un Kyu Kim
Keyword(s):  
Sectional Curvature ◽  
Complex Space ◽  
Hermitian Manifold ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Generalized Complex ◽  
Complex Forms ◽  
Complex Space Forms

AbstractWe characterize four-dimensional generalized complex forms and construct an Einstein and weakly *-Einstein Hermitian manifold with pointwise constant holomorphic sectional curvature which is not globally constant.

scholarly journals Legendrian normally flat submanifols of $\mathcal{S}$-space forms

2020 ◽  
Vol 12 (1) ◽  
pp. 69-78
Author(s):  
F. Mahi ◽  
M. Belkhelfa
Keyword(s):  
Sectional Curvature ◽  
Space Form ◽  
Space Forms ◽  
Totally Geodesic

In the present study, we consider a Legendrian normally flat submanifold $M$ of $(2n+s)$-dimensional $\mathcal{S}$-space form $\widetilde{M}^{2n+s}(c)$ of constant $\varphi$-sectional curvature $c$. We have shown that if $M$ is pseudo-parallel then $M$ is semi-parallel or totally geodesic. We also prove that if $M$ is Ricci generalized pseudo-parallel, then either it is minimal or $L=\frac{1}{n-1}$, when $c\neq -3s$.

Biharmonic hypersurfaces in pseudo-Riemannian space forms

2016 ◽  
Vol 13 (07) ◽  
pp. 1650094 ◽  
Author(s):  
Dan Yang ◽  
Yu Fu
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Constant Mean Curvature ◽  
Space Form ◽  
Constant Sectional Curvature ◽  
Principal Curvatures ◽  
Space Forms ◽  
Riemannian Space Forms

Let [Formula: see text] be a nondegenerate biharmonic pseudo-Riemannian hypersurface in a pseudo-Riemannian space form [Formula: see text] with constant sectional curvature [Formula: see text]. We show that [Formula: see text] has constant mean curvature provided that it has three distinct principal curvatures and the Weingarten operator can be diagonalizable.

Explicit construction of Lagrangian isometric immersion of a real-space-form Mn(c) into a complex-space-form M˜n(4c)

2002 ◽  
Vol 132 (3) ◽  
pp. 481-508 ◽  
Author(s):  
YUN MYUNG OH
Keyword(s):  
Sectional Curvature ◽  
Isometric Immersion ◽  
Complex Space ◽  
Space Form ◽  
Real Space ◽  
Constant Sectional Curvature ◽  
Complex Space Form ◽  
Product Decomposition ◽  
Twisted Product ◽  
Space Forms

In [4], it is proved that there exists a ‘unique’ adapted Lagrangian isometric immersion of a real-space-form Mn(c) of constant sectional curvature c into a complex-space-form M˜n(4c) of constant sectional curvature 4c associated with each twisted product decomposition of a real-space-form if its twistor form is twisted closed. Conversely, if L: Mn(c) → M˜n(4c) is a non-totally geodesic Lagrangian isometric immersion of a real-space-form Mn(c) into a complex-space-form M˜n(4c), then Mn(c) admits an appropriate twisted product decomposition with twisted closed twistor form and, moreover, the immersion L is determined by the corresponding adapted Lagrangian isometric immersion of the twisted product decomposition. It is natural to ask the explicit expressions of adapted Lagrangian isometric immersions of twisted product decompositions of real-space-forms Mn(c) into complex-space-forms M˜n(4c) for each case: c = 0, c > 0 and c < 0.

scholarly journals CR-submanifolds of a locally conformal Kaehler space form

1994 ◽  
Vol 17 (3) ◽  
pp. 511-514
Author(s):  
M. Hasan Shahid
Keyword(s):  
Scalar Curvature ◽  
Sectional Curvature ◽  
Ricci Curvature ◽  
Space Form ◽  
Holomorphic Sectional Curvature ◽  
Totally Geodesic ◽  
Locally Conformal ◽  
Cr Submanifolds

(Bejancu [1,2]) The purpose of this paper is to continue the study ofCR-submanifolds, and in particular of those of a locally conformal Kaehler space form (Matsumoto [3]). Some results on the holomorphic sectional curvature,D-totally geodesic,D1-totally geodesic andD1-minimalCR-submanifolds of locally conformal Kaehler (1.c.k.)-space fromM¯(c)are obtained. We have also discussed Ricci curvature as well as scalar curvature ofCR-submanifolds ofM¯(c).

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