On generalized weakly symmetric $(LCS)_{n}$-manifolds

Yıl 2019, Cilt: 48 Sayı: 2, 427 - 438, 01.04.2019

Kanak Kanti Baishya

Öz

The object of the present paper is to study generalized weakly symmetric and weakly Ricci symmetric $(LCS)_{n}$-manifolds. Our aim is to bring out different type of curvature restrictions for which $(LCS)_{n}$-manifolds are sometimes Einstein and some other time remain $\eta $-Einstein. Finally, the existence of such manifold is ensured by a non-trivial example.

Anahtar Kelimeler

$(LCS)_{n}$-manifold, generalized weakly symmetric manifold, Einstein space, $\eta $-Einstein space

Kaynakça

• H. Bağdatlı Yılmaz, On decomposable almost pseudo conharmonically symmetric manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 51 (1), 111- 124, 2012.
• H. Bağdatlı Yılmaz, On Almost Pseudo Quasi-Conformally Symmetric Manifolds, pre-print.
• K.K. Baishya, On generalized weakly symmetric manifolds, Bull. Transilv. Univ. Braÿsov Ser. III 10 (59), 31-38, 2017.
• K.K. Baishya, On generalized semi-pseudo symmetric manifold, submitted.
• K.K. Baishya and P.R. Chowdhury, $\eta$-Ricci solitons in $(LCS)_{n}$-manifolds, Bull. Transilv. Univ. Braÿsov Ser. III 9 (58), 1-12, 2016.
• K.K. Baishya, P.R. Chowdhury, M. Josef and P. Peska, On almost generalized weakly symmetric Kenmotsu manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 55 (2), 5-15, 2016.
• E. Cartan, Sur une classes remarquable d’espaces de Riemannian, Bull. Soc. Math. France 54, 214-264, 1926.
• M.C. Chaki, On pseudo symmetric manifolds, Analele Ştiinţifice Ale Univer˘siţatii "AL I.Cuza’" Din Iaşi 33, 53-58, 1987.
• M.C. Chaki and T. Kawaguchi, On almost pseudo Ricci symmetric manifolds, Tensor 68 (1), 10-14, 2007.
• U.C. De and S. Bandyopadhyay, On weakly symmetric spaces, Acta Math. Hung. 83, 205-212, 2000.
• R.S.D. Dubey, Generalized recurrent spaces, Indian J. Pure Appl. Math. 10 (12), 1508-1513, 1979.
• S.K. Hui and M. Atceken, Contact warped productsemi-slant submanifolds of $(LCS)_{n}$- manifolds, Acta Univ. Sapientiae Mathematica 3 (2), 212-224, 2011.
• J.P. Jaiswal and R.H. Ojha, On weakly pseudo-projectively symmetric manifolds, Differential Geometry - Dynamical Systems 12, 83-94, 2010.
• F. Malek and M. Samawaki, On weakly symmetric Riemannian manifolds, Differential Geometry - Dynamical Systems, 10, 215-220, 2008.
• C.A. Mantica and L.G. Molinari, Weakly Z-symmetric manifolds, Acta Math. Hungar. 135, 80-96, 2012.
• C.A. Mantica and L.G. Molinari, Twisted Lorentzian manifolds: a characterization with torse-forming time-like unit vectors, Gen. Relativ. Gravit. 49:51, 2017.
• C.A. Mantica and L.G. Molinari, Generalized Robertson-Walker space-times, a survey, Int. J. Geom. Meth. Mod.Phys. 14 (3), 1730001, 2017.
• C.A. Mantica and Y.J. Suh, Pseudo Z-symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Meth. Mod. Phys. 9, 1250004, 2012.
• D. Narain and S. Yadav, On weak concircular symmetries of $(LCS)_{2n+1} $-manifolds, Global Journal of Science Frontier Research 12, 85-94, 2012.
• B. O’Neill, Semi-Riemannian Geometry, Academic Press, Inc, New York, 1983.
• F. Özen and S. Altay, On weakly and pseudo symmetric Riemannian spaces, Indian J. Pure Appl. Math. 33 (10), 1477-1488, 2001.
• F. Özen and S. Altay, On weakly and pseudo concircular symmetric structures on a Riemannian manifold, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 47, 129-138, 2008.
• M. Prvanovic, On weakly symmetric riemannian manifolds, Pub. Math. Debrecen 46, 19-25, 1995.
• M. Prvanovic, On totally umbilical submanifolds immersed in a weakly symmetric riemannian manifolds, Pub. Math. Debrecen 6, 54-64, 1998.
• A.A. Shaikh, On Lorentzian almost para contact manifolds with a structure of the concircular type, Kyungpook Math. J. 43, 305-314 ,2003.
• A.A. Shaikh and K.K. Baishya, On weakly quasi-conformally symmetric manifolds, Soochow J. Math. 31 (4), 581-595, 2005.
• A.A. Shaikh and K.K. Baishya, On concircular structure spacetimes, J. Math. Stat. 1, 129-132, 2005.
• A.A. Shaikh and K.K. Baishya, On concircular structurespacetimes II, American J. Appl. Sci. 3, 1790-1794, 2006.
• A.A. Shaikh and T.Q. Binh, On weakly symmetric $(LCS)_{n}$-manifolds, J. Adv. Math. Studies 2, 75-90, 2009.
• A.A. Shaikh and S.K. Hui, On generalized $\phi$-recurrent $(LCS)_{n}$-manifolds, AIP Conference Proceedings 1309, 419-429, 2010.
• A.A. Shaikh and S.K. Jana, On weakly symmetric manifolds, Publ. Math. Debrecen 71 (1-2), 2007.
• A.A. Shaikh, I. Roy and S.K. Hui, On totally umbilical hypersurfaces of weakly conharmonically symmetric spaces, Global Journal of Science Frontier Research 10 (4), 28-31, 2010.
• G.T. Sreenivasa, Venkatesha and C.S. Bagewadi, Some results on $(LCS)_{2n+1}$-manifolds, Bull. Math. Anal. Appl. 3 (1), 64-70, 2009.
• L. Tamássy and T.Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloq. Math. Soc. János Bolyai 56, 663-670, 1989.
• M. Tarafdar and M.A.A. Jawarneh, Semi-Pseudo Ricci Symmetric manifold, J. Indian. Inst. Sci. 73, 591-596, 1993.
• A.G. Walker, On Ruse’s space of recurrent curvature, Proc. London Math. Soc. 52, 36-54, 1950.
• K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics 3, World Scientific Publishing, 1985.