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Year 2013, Volume 3, Issue 1, 108 - 116, 01.06.2013

Abstract

References

  • [1] Gray, A. and Hervella, L. M., (1980), The sixteen classes of almost Hermitian manifolds and their liner invariants, Ann, Mat. Pura Appl., 123 (4), 35-58.
  • [2] Chen, B. Y., (1981), Geometry of submanifolds and its applications, Sci. Univ. Tokyo, Tokyo.
  • [3] Blair, D. E., (1976), Contact manifolds in Riemannian geometry, Lecture Notes in Math., 509, Springer Verlag.
  • [4] Blair, D. E. and Oubina, J. A., (1990), Conformal and related changes of metric on the product of two almost contact metric manifolds, Publications Matematiques 34, 199-207.
  • [5] Chinea, D. and Perestelo, P. S., (1991), Invariant submnifolds of a trans-Contact manifold, Publ. Math. Debrecen, 38, 103-109, MR 92 g: 53025.
  • [6] Janssens, D. and Vanhecke, L., (1981), Almost contact strucures and curvature tensors, Kodai Math. J., 4, 1-27.
  • 7] Oubina, J. A., (1985), New classes of almost contact metic structures, Publ. Math. Debrecen, 32, 187-193.
  • [8] Marrero, J. C., (1992), The local structure of trans-Contact manifolds, Ann. Mat. Pura Appl., 162 (4), 77-86, MR 93j:53044.
  • [9] Sengupta, J. and Biswas, B., (2003), Quarter-symmetric non-metric connection on a Sasakian manifold, Bull. Cal. Math. Soc., 95 (2), 169-176.
  • [10] Kenmotsu, K., (1972), A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, 93-103.
  • [11] Yano, K. and Imai, T., (1982), Quarter-symmetric metric connections and their curvature tensors, Tensor, (N. S.), 38, 13-18.
  • [12] Bhatt, L. and Dubey, K. K., (2003), On CR-submanifold of trans hyperbolic Contact manifold, Acta Cieme. Indica, 29 (1), 91-96.
  • [13] Upadhyay, M. D. and Dubey, K. K., (1976), Almost Contact hyperbolic (f,g,η,ξ)- structure, Acta Math. Acad. Scient Hung., 28, 13-15.
  • [14] Singh, R. N. and Pandey, M. K., (2007), On a type of quarter-symmetric non-metric connection in a Kenmotsu manifold, Bull. Cal. Math. Soc., 99 (4), 433-444.
  • [15] Mishra, R. S. and Pandey, S. N., (1980), On quarter symmetric metric F-connections, Tensor, (N. S.), 34 (1), 1-7.
  • [16] Mishra, R. S., (1991), Almost contact metric manifolds, Monograph 1, Tensor society of India, Lucknow.
  • [17] Prasad, R., Tripathi, M. M. and Kim, J.-S., (2002), On generalized recci-recurrent trans contact manifolds, J. Korean Math. Soc., 39 (6), 953-961.
  • [18] Prasad, R., Tripathi, M. M. and Kim, J.-S., (2002), J-H Cho, On automorphism groups of an 2 framed manifold, Commun. Korean Math. Soc., 17 (4), 635-645.
  • [19] Prasad, R. and Tripathi, M. M., (2003), ξ-horizontal hyper surfaces of Kemmotsu manifolds, Bull. Cal. Math. Soc., 95 (2), 121-126.
  • [20] Prasad, R. and Tripathi, M. M., (2002), On non-invariant hyper surface of Trans-Contact manifolds, J. Int. Acad. Physical. Sci., 6 (1), 33-40.
  • [21] Prasad, R. and Tripathi, M. M., (2003), Transversal hyper surface of Kenmotsu manifold, Indian J. Pure Appl. Math., 34 (3), 443-452.
  • [22] Biswas, S. C. and De, U. C., (1997), Quarter-symmetric metric connection in an SP-Sasakian manifold, Common. Fac. Sci. Univ. Ank. Al., 46, 49.
  • [23] Golab, S., (1975), On semi-symmetric and quarter symmetric linear connections, Tensor, (N.S.), 29 (3), 249-254.
  • [24] Rastogi, S. C., (1978), On quarter symmetric non metric connection, C. R. Acad. Bulgare Sci., 31 (7), 811-814.
  • [25] Rastogi, S. C., (1987), On quarter-symmetric metric connection, Tensor, (N. S.), 44, 133-141.
  • [26] Kanemaki, S., (1984), On quasi-Contact manifolds, Diff. Geometry Banach Center Publications, 12, 95-125.
  • [27] Mukhopadhyay, S., Ray, A. K. and Barua, B., (1991), Some properties of a quarter-symmetric metric connection on a Riemannian manifold, Soochow J. of Math., 17 (2), 205.
  • [28] Tanno, S., (1969), The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 21, 21-38.
  • [29] Ki, U. H., Pak, J. S. and Suh, H. B., (1975), On (f, g, u(k), α(k))-structures, Kodai Math. Sem. Rep, 26, 160-175.

TRANSVERSAL HYPERSURFACES OF ALMOST HYPERBOLIC CONTACT MANIFOLDS WITH A QUARTER SYMMETRIC NON METRIC CONNECTION

Year 2013, Volume 3, Issue 1, 108 - 116, 01.06.2013

Abstract

Transversal hypersurfaces of trans hyperbolic contact manifolds endowed with a quarter symmetric non metric connection are studied. It is proved that transversal hypersurfaces of almost hyperbolic contact manifold with a quarter symmetric non metric connection admits an almost product structure and each transversal hypersurfaces of almost hyperbolic contact metric manifold with a quarter symmetric non metric connection admits an almost product semi-Riemannian structure. The fundamental 2- form on the transversal hypersurfaces of cosymplectic hyperbolic manifold and α, 0 trans hyberbolic Sasakian manifold with hyperbolic f, g, u, v, α -structure are closed. It is also proved that transversal hypersurfaces of trans hyperbolic contact manifold with a quarter symmetric non metric connection admits a product structure. Some properties of transversal hypersurfaces with a quarter symmetric non metric connection are proved.

References

  • [1] Gray, A. and Hervella, L. M., (1980), The sixteen classes of almost Hermitian manifolds and their liner invariants, Ann, Mat. Pura Appl., 123 (4), 35-58.
  • [2] Chen, B. Y., (1981), Geometry of submanifolds and its applications, Sci. Univ. Tokyo, Tokyo.
  • [3] Blair, D. E., (1976), Contact manifolds in Riemannian geometry, Lecture Notes in Math., 509, Springer Verlag.
  • [4] Blair, D. E. and Oubina, J. A., (1990), Conformal and related changes of metric on the product of two almost contact metric manifolds, Publications Matematiques 34, 199-207.
  • [5] Chinea, D. and Perestelo, P. S., (1991), Invariant submnifolds of a trans-Contact manifold, Publ. Math. Debrecen, 38, 103-109, MR 92 g: 53025.
  • [6] Janssens, D. and Vanhecke, L., (1981), Almost contact strucures and curvature tensors, Kodai Math. J., 4, 1-27.
  • 7] Oubina, J. A., (1985), New classes of almost contact metic structures, Publ. Math. Debrecen, 32, 187-193.
  • [8] Marrero, J. C., (1992), The local structure of trans-Contact manifolds, Ann. Mat. Pura Appl., 162 (4), 77-86, MR 93j:53044.
  • [9] Sengupta, J. and Biswas, B., (2003), Quarter-symmetric non-metric connection on a Sasakian manifold, Bull. Cal. Math. Soc., 95 (2), 169-176.
  • [10] Kenmotsu, K., (1972), A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, 93-103.
  • [11] Yano, K. and Imai, T., (1982), Quarter-symmetric metric connections and their curvature tensors, Tensor, (N. S.), 38, 13-18.
  • [12] Bhatt, L. and Dubey, K. K., (2003), On CR-submanifold of trans hyperbolic Contact manifold, Acta Cieme. Indica, 29 (1), 91-96.
  • [13] Upadhyay, M. D. and Dubey, K. K., (1976), Almost Contact hyperbolic (f,g,η,ξ)- structure, Acta Math. Acad. Scient Hung., 28, 13-15.
  • [14] Singh, R. N. and Pandey, M. K., (2007), On a type of quarter-symmetric non-metric connection in a Kenmotsu manifold, Bull. Cal. Math. Soc., 99 (4), 433-444.
  • [15] Mishra, R. S. and Pandey, S. N., (1980), On quarter symmetric metric F-connections, Tensor, (N. S.), 34 (1), 1-7.
  • [16] Mishra, R. S., (1991), Almost contact metric manifolds, Monograph 1, Tensor society of India, Lucknow.
  • [17] Prasad, R., Tripathi, M. M. and Kim, J.-S., (2002), On generalized recci-recurrent trans contact manifolds, J. Korean Math. Soc., 39 (6), 953-961.
  • [18] Prasad, R., Tripathi, M. M. and Kim, J.-S., (2002), J-H Cho, On automorphism groups of an 2 framed manifold, Commun. Korean Math. Soc., 17 (4), 635-645.
  • [19] Prasad, R. and Tripathi, M. M., (2003), ξ-horizontal hyper surfaces of Kemmotsu manifolds, Bull. Cal. Math. Soc., 95 (2), 121-126.
  • [20] Prasad, R. and Tripathi, M. M., (2002), On non-invariant hyper surface of Trans-Contact manifolds, J. Int. Acad. Physical. Sci., 6 (1), 33-40.
  • [21] Prasad, R. and Tripathi, M. M., (2003), Transversal hyper surface of Kenmotsu manifold, Indian J. Pure Appl. Math., 34 (3), 443-452.
  • [22] Biswas, S. C. and De, U. C., (1997), Quarter-symmetric metric connection in an SP-Sasakian manifold, Common. Fac. Sci. Univ. Ank. Al., 46, 49.
  • [23] Golab, S., (1975), On semi-symmetric and quarter symmetric linear connections, Tensor, (N.S.), 29 (3), 249-254.
  • [24] Rastogi, S. C., (1978), On quarter symmetric non metric connection, C. R. Acad. Bulgare Sci., 31 (7), 811-814.
  • [25] Rastogi, S. C., (1987), On quarter-symmetric metric connection, Tensor, (N. S.), 44, 133-141.
  • [26] Kanemaki, S., (1984), On quasi-Contact manifolds, Diff. Geometry Banach Center Publications, 12, 95-125.
  • [27] Mukhopadhyay, S., Ray, A. K. and Barua, B., (1991), Some properties of a quarter-symmetric metric connection on a Riemannian manifold, Soochow J. of Math., 17 (2), 205.
  • [28] Tanno, S., (1969), The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 21, 21-38.
  • [29] Ki, U. H., Pak, J. S. and Suh, H. B., (1975), On (f, g, u(k), α(k))-structures, Kodai Math. Sem. Rep, 26, 160-175.

Details

Primary Language English
Journal Section Research Article
Authors

Shamsur RAHMAN This is me
Department of Mathematics, Maulana Azad National Urdu University Polytechnic, Darbhanga (Branch) Bihar 846001, India

Publication Date June 1, 2013
Published in Issue Year 2013, Volume 3, Issue 1

Cite

Bibtex @ { twmsjaem761700, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2013}, volume = {3}, number = {1}, pages = {108 - 116}, title = {TRANSVERSAL HYPERSURFACES OF ALMOST HYPERBOLIC CONTACT MANIFOLDS WITH A QUARTER SYMMETRIC NON METRIC CONNECTION}, key = {cite}, author = {Rahman, Shamsur} }