On $\varphi$-${\cal T}$-Symmetric ($\varepsilon$)-Para Sasakian Manifolds

Punam Gupta

Abstract


The purpose of the present paper is to study the globally and locally ϕ-T-symmetric (ε)-para Sasakian manifold. The globally ϕ-T-symmetric (ε)-para Sasakian manifold is either Einstein manifold or has a constant scalar curvature. The necessary and sufficient condition for Einstein manifold to be globally ϕ-T -symmetric is given. A 3-dimensional (ε) -para Sasakian manifold is locally ϕ-T-symmetric if and only if the scalar curvature r is constant. A 3-dimensional (ε)-para Sasakian manifold with η-parallel Ricci tensor is locally ϕ-T-symmetric. In the last, an example of 3-dimensional locally ϕ-T-symmetric (ε)-para Sasakian manifold is given.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|