On weakly symmetric generalized trans-sasakian manifold

• Autorzy: Das, L. S. , Nivas, R. , Agnihotri, R.
• 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 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.

Słowa kluczowe

EN

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

• Czasopismo: Commentationes Mathematicae
• Rocznik: 2014
• Tom: Vol 54, No. 1
• Strony: 141--145
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Das, L. S.

• Department of Mathematics, Kent State University New Philadelphia, OH 44663, U.S.A.,

autor

Nivas, R.

• Department of Mathematics and Astronomy, Lucknow University Lucknow-226007, India,

autor

Agnihotri, R.

• Department of Mathematics and Astronomy, Lucknow University Lucknow-226007, India,

Bibliografia

• [1] L. Tamassy and T. Q. Binh: On wealy symmetric and weakly projective symmetric Riemannian manifold, Colloq. Math. Janos Bolayi 56 (1989), 663–670.
• [2] U. C. De and M. M. Tripathi: Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math. J. 43 (2003), 1–9.
• [3] M.C. Chaki: On pseudo Ricci symmetric manifolds, Bulg. J. Phys. 15 (1988), 526–531.
• [4] S. Sasaki: Lecture Notes on Almost contact manifolds Part I, Tohoku University, Tohoku, 1965.
• [5] S. Sasaki: Lecture Notes on Almost contact manifolds Part II, Tohoku University, Tohoku, 1967.
• [6] D. E. Blair: Contact manifold in Riemannian geometry, Lecture Notes in Mathematics no. 509, Springer Verlag, 1966.

Identyfikatory

DOI

10.14708/cm.v54i1.767