scholarly journals Geodesic spheres in a nonflat complex space form and their integral curves of characteristic vector fields

2007 ◽  
Vol 36 (2) ◽  
pp. 353-363
Author(s):  
Sadahiro MAEDA ◽  
Toshiaki ADACHI ◽  
Young Ho KIM
Keyword(s):  
Vector Fields ◽  
Complex Space ◽  
Space Form ◽  
Characteristic Vector ◽  
Complex Space Form ◽  
Geodesic Spheres ◽  
Integral Curves ◽  
Characteristic Vector Fields

scholarly journals On pseudo-Einstein real hypersurfaces

2020 ◽  
Vol 20 (4) ◽  
pp. 559-571
Author(s):  
Mayuko Kon
Keyword(s):  
Ricci Tensor ◽  
Real Hypersurface ◽  
Vector Fields ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Definition Of ◽  
Weaker Conditions

AbstractLet M be a real hypersurface of a complex space form Mn(c) with c ≠ 0 and n ≥ 3. We show that the Ricci tensor S of M satisfies S(X, Y) = ag(X, Y) for all vector fields X and Y on the holomorphic distribution, a being a constant, if and only if M is a pseudo-Einstein real hypersurface. By doing this we can give the definition of pseudo-Einstein real hypersurface under weaker conditions.

scholarly journals Length spectrum of geodesic spheres in a non-flat complex space form

2002 ◽  
Vol 54 (2) ◽  
pp. 373-408 ◽  
Author(s):  
Toshiaki ADACHI ◽  
Sadahiro MAEDA ◽  
Masakazu YAMAGISHI
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Length Spectrum ◽  
Complex Space Form ◽  
Geodesic Spheres

scholarly journals Characteristic Lightlike Submanifolds of an IndefiniteS-Manifold

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Jae Won Lee
Keyword(s):  
Vector Fields ◽  
Space Form ◽  
Characteristic Vector ◽  
Indefinite Metric ◽  
Totally Umbilical ◽  
Screen Distribution ◽  
Lightlike Submanifolds ◽  
Characteristic Vector Fields

We study characteristicr-lightlike submanifoldsMtangent to the characteristic vector fields in an indefinite metricS-manifold, and we also discuss the existence of characteristic lightlike submanifolds of an indefiniteS-space form under suitable hypotheses: (1)Mis totally umbilical or (2) its screen distributionS(TM)is totally umbilical inM.

scholarly journals Generating Curves of Minimal Ruled Real Hypersurfaces in a Nonflat Complex Space Form

2019 ◽  
Vol 62 (02) ◽  
pp. 383-392 ◽  
Author(s):  
Sadahiro Maeda ◽  
Hiromasa Tanabe ◽  
Seiichi Udagawa
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Ruled Real Hypersurfaces ◽  
Integral Curves ◽  
Necessary And Sufficient ◽  
Characteristic Vector Field ◽  
Ruled Real Hypersurface

AbstractWe first provide a necessary and sufficient condition for a ruled real hypersurface in a nonflat complex space form to have constant mean curvature in terms of integral curves of the characteristic vector field on it. This yields a characterization of minimal ruled real hypersurfaces by circles. We next characterize the homogeneous minimal ruled real hypersurface in a complex hyperbolic space by using the notion of strong congruency of curves.

scholarly journals Real hypersurfaces in a complex space form with a condition on the structure Jacobi operator

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
S. Kon ◽  
Tee-How Loo ◽  
Shiquan Ren
Keyword(s):  
Vector Fields ◽  
Complex Space ◽  
Space Form ◽  
Jacobi Operator ◽  
Hyperbolic Spaces ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
The Real ◽  
Complex Projective

AbstractIn this paper we classify the real hypersurfaces in a non-flat complex space form with its structure Jacobi operator R ξ satisfying (∇X R ξ)ξ = 0, for all vector fields X in the maximal holomorphic distribution D. With this result, we prove the non-existence of real hypersurfaces with D-parallel as well as D-recurrent structure Jacobi operator in complex projective and hyperbolic spaces. We can also prove the non-existence of real hypersurfaces with recurrent structure Jacobi operator in a non-flat complex space form as a corollary.

scholarly journals CR-warped product submanifolds of a generalized complex space form

2017 ◽  
Vol 4 (1) ◽  
pp. 1306153
Author(s):  
Meraj Ali Khan ◽  
Amira A. Ishan ◽  
Hari M. Srivastava
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Generalized Complex
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