On weakly symmetric generalized Trans-Sasakian manifold

• Autorzy: Lovejoy S. Das
• Języki publikacji: EN

Abstrakty

EN

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 \(\gamma\neq\tau\).

Słowa kluczowe

EN

Trans-Sasakian manifold; weakly symmetric; Riemannian manifold; curvature tensor

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2015
• Tom: 55
• Numer: 1

Daty

wydano

2015

online

2015-08-07

Twórcy

autor

Lovejoy S. Das

Identyfikatory

DOI

10.14708/cm.v55i1.811