On weakly symmetric generalized Trans-Sasakian manifold

Lovejoy S. Das. "On weakly symmetric generalized Trans-Sasakian manifold." Commentationes Mathematicae 55.1 (2015): null. <http://eudml.org/doc/292386>.

@article{LovejoyS2015,
abstract = {In this paper, we have defined the weakly symmetric generalized Trans-Sasakian manifold $G(WS)_n$ and it has been shown that on such manifold if any two of the vector field $\lambda ,\gamma ,\tau $ defined by equation \[ A(X)=g(X,\lambda ), B(X)=g(X,\mu ), C(X)=g(X,\gamma ), D(X)=g(X,\tau ) \] are orthogonal to $\xi $, then the third will also be orthogonal to $\xi $. We have also proved that the scalar curvature $r$ of weakly symmetric generalized Trans-Sasakian manifold $G(WS)_n$, $(n>2)$ satisfies the equation $r=2n(\alpha ^2-\beta ^2)$, where $\alpha $ and $\beta $ are smooth function and $\gamma \ne \tau $.},
author = {Lovejoy S. Das},
journal = {Commentationes Mathematicae},
keywords = {Trans-Sasakian manifold; weakly symmetric; Riemannian manifold; curvature tensor},
language = {eng},
number = {1},
pages = {null},
title = {On weakly symmetric generalized Trans-Sasakian manifold},
url = {http://eudml.org/doc/292386},
volume = {55},
year = {2015},
}

TY - JOUR
AU - Lovejoy S. Das
TI - On weakly symmetric generalized Trans-Sasakian manifold
JO - Commentationes Mathematicae
PY - 2015
VL - 55
IS - 1
SP - null
AB - In this paper, we have defined the weakly symmetric generalized Trans-Sasakian manifold $G(WS)_n$ and it has been shown that on such manifold if any two of the vector field $\lambda ,\gamma ,\tau $ defined by equation \[ A(X)=g(X,\lambda ), B(X)=g(X,\mu ), C(X)=g(X,\gamma ), D(X)=g(X,\tau ) \] are orthogonal to $\xi $, then the third will also be orthogonal to $\xi $. We have also proved that the scalar curvature $r$ of weakly symmetric generalized Trans-Sasakian manifold $G(WS)_n$, $(n>2)$ satisfies the equation $r=2n(\alpha ^2-\beta ^2)$, where $\alpha $ and $\beta $ are smooth function and $\gamma \ne \tau $.
LA - eng
KW - Trans-Sasakian manifold; weakly symmetric; Riemannian manifold; curvature tensor
UR - http://eudml.org/doc/292386
ER -