Arpan Sardar

DOI Number
First page
Last page


We have studied curvature symmetries in ($\epsilon$)-Kenmotsu manifolds. Next, we have proved the non-existence of a non-zero parallel 2-form in an ($\epsilon$)-Kenmotsu manifold. Moreover, we have characterised $\phi$-Ricci symmetric ($\epsilon$)-Kenmotsu manifolds and finally, we have proved that under certain restriction on the scalar curvature $divR$=0 and $divC$=0 are equivalent, where `$div$' denotes divergence.


{($\epsilon$)-Kenmotsu manifold, curvature symmetries, $\phi$-Ricci symmetric manifold, Weyl curvature tensor.

Full Text:



bibitem{bb}{sc A. Bejancu {rm and} K. L. Duggal}: textit{Real hypersurfaces of indefinite K{"a}hler manifolds}, Pacific J. Math. {bf 16}(1993), 545--556.

bibitem{ken} {sc A. M. Blaga}: {itshape $eta$-Ricci solitons on para-Kenmotsu manifolds}, Balkan J. Geom. Applicat. {bf 20}(2015), 1-13.

bibitem{chen} {sc U. C. De {rm and} A. Sarkar }: {itshape On ($epsilon$)-Kenmotsu manifold}, Hardonic J. {bf 32}(2009), 231-242.

bibitem{bla1} {sc K. L. Duggal}: {itshape Space time manifold and contact structures}, Internat. J. Math and Math Sci., {bf 16}(1990), 545-553.

bibitem{neill} {sc K. L. Duggal {rm and} R. Sharma}: {itshape Symmetries of space time and Riemannian manifolds}, Kluwer Acad. Publishers, 1999.

bibitem{desh1} {sc L. P. Eisenhart}: {itshape Symmetric tensor of the second order whose first covariant derivatives are zero}, Tran. Amer. Math. Soc. {bf 25}(1923), 297-306.

bibitem{desh2} {sc A. Haseeb {rm and} U. C. De}: {itshape $eta$-Ricci solitions in ($epsilon$)-Kenmotsu manifolds}, J. Geom. {bf 110}(2019), 1-12.

bibitem{de1} {sc A. Haseeb, M. K. Khan {rm and} M. D. Siddiqi}: {itshape Some more results on an ($epsilon$)-Kenmotsu manifold with a semi-symmetric metric connenction}, Acta. Math. Univ. Comenianae, {bf LXXXV}(2016), 9-20.

bibitem{dugg} {sc A. Haseeb}: {itshape Some results on projective curvature tensor in an ($epsilon$)-Kenmotsu manifold}, Palestine J. Math. {bf 6}(2017), 196-203.

bibitem{bla2} {sc K. Kenmotsu}: {itshape A class of almost contact Riemannian manifolds}, Tohoku Math J. {bf 24}(1972), 93-103.

bibitem{ivey} {sc R. Sharma {rm and} K. L. Duggal}: {itshape A characterization of an affine conformal vector field}, C.R. Math. Rep. Acad. Sci. Canada {bf 7}(1985), 201-205.

bibitem{fri} {sc R. Sharma}: {itshape On the curvature of contact metric manifold}, J. Geom. {bf 53}(1995), 179-190.

bibitem{de2} {sc R. N. Sing, S. K. Pandey, G. Pandey {rm and} K. Tiwari}: {itshape On a semi-symmetric metric connention in an ($epsilon$)-Kenmotsu manifold}, Commun. Korean Math. Soc. {bf 29}(2014), 331-343.

bibitem{hamilton2} {sc T. Takahasi}: {itshape Sasakian $phi$-symmetric spaces}, Tohoku Math. J. {bf 29}(1977), 91-113.

bibitem{hamilton1} {sc V. Venkatesha {rm and} S. V. Vishnuvardhana}: {itshape ($epsilon$)-Kenmotsu manifolds admiting a semi-symmetric connection}, Italian J. Pure Appl. Math. {bf 38}(2017), 615-623.

bibitem{bej} {sc X. Xufeng {rm and} C. Xiaoli}: {itshape Two therems on ($epsilon$)-Sasakian manifolds}, Internat. J. Math. Math Sci., {bf 21}(1998), 249-254.



© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)