# On weakly symmetric generalized trans-sasakian manifold

Levejoy S. Das; Ram Nivas; Rupali Agnihotri

Commentationes Mathematicae (2014)

- Volume: 54, Issue: 1
- ISSN: 2080-1211

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topLevejoy S. Das, Ram Nivas, and Rupali Agnihotri. "On weakly symmetric generalized trans-sasakian manifold." Commentationes Mathematicae 54.1 (2014): null. <http://eudml.org/doc/292534>.

@article{LevejoyS2014,

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 fields $\lambda ,\gamma ,\tau $, defined by equation (0.3) 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 = {Levejoy S. Das, Ram Nivas, Rupali Agnihotri},

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/292534},

volume = {54},

year = {2014},

}

TY - JOUR

AU - Levejoy S. Das

AU - Ram Nivas

AU - Rupali Agnihotri

TI - On weakly symmetric generalized trans-sasakian manifold

JO - Commentationes Mathematicae

PY - 2014

VL - 54

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 fields $\lambda ,\gamma ,\tau $, defined by equation (0.3) 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/292534

ER -

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