On generalized pseudo conformally symmetric manifolds

Akshoy Patra

doi:10.26637/mjm1204/009

Abstract

In this paper, a type of Riemannian manifold, namely generalized pseudo conformally symmetric manifold is studied. Several geometric properties of such spaces are studied. By imposing different restrictions on the conformal curvature tensor, we have obtained several properties. If the conformal curvature tensor is harmonic, then the form of the scalar curvature is obtained. Also, the relations among the 1-forms under various conditions are obtained.

Keywords:

Pseudo symmetry, Second Bianchi Identity, Conformal curvature tensor, Harmonic curvature tensor

Mathematics Subject Classification:

53C20, 53C21, 53C44

Authors Imprint References Funding Related Articles Downloads

Akshoy Patra Government College of Enggineering and Textile Technology, Berhampore, 742101, Dist. Murshidabad, West Bengal, India.

Pages: 457-463
Date Published: 03-12-2024
Vol. 12 No. 04 (2024): Malaya Journal of Matematik (MJM)

M. Ali, Q. Khan, M. Vasiulla, On generalized pseudo symmetric manifolds,Bull. Cal. Math. Soc., 113(4) (2021), 353-362.

É. Cartan, Sur une classe remarquable d'espaces de Riemann, I,Bull. de la Soc. Math. de France, 54, (1926), 214-216. DOI: https://doi.org/10.24033/bsmf.1105

É. Cartan, Sur une classe remarquable d'espaces de Riemann, II, Bull. de la Soc. Math. de France, 55, (1927), 114-134. DOI: https://doi.org/10.24033/bsmf.1113

M. C. Chakı, On pseudosymmetric manifolds,An. Sti. Ale Univ., "AL. I. CUZA" Din Ias, 33 (1987), 53-58.

M. C. Chakı, On pseudosymmetric Ricci symmetric manifolds, Bulg. J. Phys., 15 (1988), 526-531.

M. C. Chakı, On generalized pseudo-symmetric manifolds, Publ. Math. Debrecen, 45 (1994), 305-312. DOI: https://doi.org/10.5486/PMD.1994.1441

R. Deszcz, On pseudosymmetric spaces,Bull. Soc. Math. Belg. Sér. A, 44 No. 1, (1992), 1-34.

Y. IshiI, On conharmonic transformations, Tensor, N. S., 11, (1957), 73-80.

J. Kim, A type of conformal curvature tensor,Far East J. Math. Sci., 99 No. 1, (2016), 61-74. DOI: https://doi.org/10.17654/MS099010061

J. Kim, On pseudo semi-conformal symmetric manifolds,Bull. Korean. Math. Soc., 54 ,(2017), 177-186. DOI: https://doi.org/10.4134/BKMS.b151007

A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc., 20 ,(1956), 47-87.

A. A. Shaikh, R. Deszcz, M. Hotloś, J. Jelowicki, H. Kundu, On pseudosymmetric manifolds,Publ. Math. Debrecen, 86(3-4), (2015), 433-456. DOI: https://doi.org/10.5486/PMD.2015.7057

A. A. ShaIкн, S. K. Hui, On weakly conharmonically symmetric manifolds,Tensor, N. S., 70, No. 2, (2008), 119-134.

A. A. ShaIKh, H. Kundu, On equivalency of various geometric structures, J. Geom., 105, (2014), 139-165. DOI: https://doi.org/10.1007/s00022-013-0200-4

A. A. Shaikh, I. Roy, S. K. Hui, On totally umbilical hypersurfaces of weakly conharmonically symmetric spaces, Global J. Science Frontier Research, 10(4), (2010), 28-31.

L. Tamássy, T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds,Coll. Math. Soc., J. Bolyai, 56, (1989), 663-670.

Z. I. Szabó, Stucture theorems on Riemannian spaces satisfying $R(X, Y) cdot R=0$, I, The local version, $J$. Diff. Geom., 17, (1982), 531-582. DOI: https://doi.org/10.4310/jdg/1214437486

A. G. Walker, On Ruse's space of recurrent curvature ,Proc. of London Math. Soc., 52 , (1950), 36-54. DOI: https://doi.org/10.1112/plms/s2-52.1.36