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On weakly symmetric generalized trans-sasakian manifold

Das L. S., Nivas R., Agnihotri R.

Commentationes Mathematicae

2014

Vol 54, No. 1

141--145

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 λ,γ,τ, defined by equation (0.3) are orthogonal to ξ, then the third will also be orthogonal to ξ. 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(α2−β2), where α and β are smooth function and γ≠τ.

On semi-invariant submanifolds of a nearly trans-Sasakian manifold admitting a semi-symmetric semi-metric connection

Das L. S., Ahmad M., Danish Siddiqi M., Haseeb A.

Demonstratio Mathematica

2013

Vol. 46, nr 2

345--359

We define a semi-symmetric semi-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a semi-symmetric semi-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.