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On weakly symmetric generalized Trans-Sasakian manifold

100%

Das L. S.

Commentationes Mathematicae

2015

tom 55

nr 1

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 $\gamma\neq\tau$.

Hypersurfaces with parallel affine curvature tensor R*

100%

Opozda B., Verstraelen L.

Annales Polonici Mathematici

1999

tom 72

nr 1

25-32

In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space $ℝ^{n+1}$. In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Commentationes Mathematicae

1 Das L. S.

1 Opozda B.

1 Verstraelen L.

1 2015

1 1999

Wyniki wyszukiwania

On weakly symmetric generalized Trans-Sasakian manifold

Hypersurfaces with parallel affine curvature tensor R*