scholarly journals Real hypersurfaces in complex two-plane Grassmannians with recurrent Ricci tensor

2015 ◽  
Vol 12 (09) ◽  
pp. 1550086 ◽  
Author(s):  
Young Jin Suh ◽  
Doo Hyun Hwang ◽  
Changhwa Woo
Keyword(s):  
Ricci Tensor ◽  
Real Hypersurfaces ◽  
Curvature Condition ◽  
Existence Property

In this paper, we have introduced a new notion of generalized Tanaka–Webster Reeb recurrent Ricci tensor of real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2). Next, we show a non-existence property for real hypersurfaces M in G2(ℂm+2) with such a curvature condition.

scholarly journals Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

2018 ◽  
Vol 61 (3) ◽  
pp. 543-552
Author(s):  
Imsoon Jeong ◽  
Juan de Dios Pérez ◽  
Young Jin Suh ◽  
Changhwa Woo
Keyword(s):  
Vector Field ◽  
Differential Operator ◽  
Ricci Tensor ◽  
Real Hypersurface ◽  
Real Hypersurfaces ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Lie Derivatives ◽  
Lie Derivation

AbstractOn a real hypersurface M in a complex two-plane Grassmannian G2() we have the Lie derivation and a differential operator of order one associated with the generalized Tanaka–Webster connection . We give a classification of real hypersurfaces M on G2() satisfying , where ξ is the Reeb vector field on M and S the Ricci tensor of M.

scholarly journals η-Ricci Solitons on Sasakian 3-Manifolds

2017 ◽  
Vol 55 (2) ◽  
pp. 143-156
Author(s):  
Pradip Majhi ◽  
Uday Chand De ◽  
Debabrata Kar
Keyword(s):  
Ricci Tensor ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Curvature Condition ◽  
Cyclic Parallel Ricci Tensor ◽  
Codazzi Type ◽  
Parallel Ricci Tensor

AbstractIn this paper we studyη-Ricci solitons on Sasakian 3-manifolds. Among others we prove that anη-Ricci soliton on a Sasakian 3-manifold is anη-Einstien manifold. Moreover we considerη-Ricci solitons on Sasakian 3-manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Beside these we study conformally flat andφ-Ricci symmetricη-Ricci soliton on Sasakian 3-manifolds. Alsoη-Ricci soliton on Sasakian 3-manifolds with the curvature conditionQ.R= 0 have been considered. Finally, we construct an example to prove the non-existence of properη-Ricci solitons on Sasakian 3-manifolds and verify some results.

Sign in / Sign up

Export Citation Format

Share Document