Geometry of Warped Product CR-Submanifolds in Kaehler Manifolds

By Bang‐Yen Chen. 2001

323 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/aaf7a5863034e6a1db007ddca5f6660f92b56209

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

Warped product submanifolds of Kaehler manifolds with a slant factor (2009, background): “[7] B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh.”
Contact CR-Warped Product Submanifolds in Sasakian Manifolds (2003, background): “squared norm of the second fundamental form khk 2 (see [ 4 ]).”
CR-Warped Products in Complex Projective Spaces with Compact Holomorphic Factor (2004, background): “A submanifold of a Kaehler manifold is called a CR-warped product if it is the warped product NT f N? of a complex submanifold NT and a totally real submanifold N? (see [5]).”
Warped Product Pointwise Bi-slant Submanifolds of Kaehler Manifolds (2017, background): “For a warped product M = M1 ×f M2, the base manifold M1 is totally geodesic in M and the fiber M2 is totally umbilical in M (see [3, 7]).”
Contact CR-Warped Product Submanifolds in Sasakian Space Forms (2004, background): “squared norm of the second fundamental form khk 2 (see [ 6 ]).”
Warped Product Pointwise Semi-slant Submanifolds of Kaehler Manifolds (2013, background): “In [5], Chen (see also, [6], [7]) studied warped product CR-submanifolds and showed that there exist no warped product CR-submanifolds of the form M⊥ ×f MT such that M⊥ is a totally real submanifold and MT is a holomorphic submanifold of a Kaehler manifold M̄ .”
Non-existence of Warped Product Semi-Slant Submanifolds of Kaehler Manifolds (2006, background): “Recently, Chen [6, 7 ] considered warped product CR-submanifolds of Kaehler manifolds and showed that there do not exist warped product CR-submanifolds in the from M⊥ ×f MT such that MT is a holomorphic (complex) submanifold and M⊥ is a totally real submanifold of a Kaehler manifold ¯”
GEOMETRY OF WARPED PRODUCTS AS RIEMANNIAN SUBMANIFOLDS AND RELATED PROBLEMS (2002, background): “6.([20]) A CR-warped product NT ×f N⊥ in CHm(−4) satisfies the basic equality ||σ||2 = 2p||∇(ln f)||2 if and only if one of the following two cases occurs: (1) NT is an open portion of complex Euclidean h-space C , N⊥ is an open portion of a unit p-sphere S and, up to rigid motions, the immersion is”