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HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE

Year 2014, , 99 - 105, 01.06.2014
https://doi.org/10.36753/mathenot.207636

Abstract

We consider some curvature conditions on the Pseudo projectivecurvature tensor P on a hypersurface in the semi-Euclidean space En+1. Wes prove that every pseudo projectively Ricci-semisymmetric hypersurface M satisfying the condition P · R = 0 is pseudosymmetric. We also consider thecondition P · S = 0 on hypersurfaces of the semi-Euclidean space En+1.s

References

  • Abdalla B.E., Dillen F.A., A Ricci-semi-symmetric hypersurface of Euclidean space which is not semi-symmetric. Proc Amer Math Soc. 130, 1805.(2002).
  • Defever F., Deszcz R., Dhooghe, P., Verstraelen L., Yaprak S¸., On Ricci-pseudosymmetric hypersurfaces in spaces of constant curvature. Results in Math. 27, 227-236 (1995).
  • Deszcz R., On certain classes of hypersurfaces in space of constant curvature. Geometry and Topology of Submanifolds VIII, World .Sci., Singapore. 101-110 (1996).
  • Deszcz R.,Glogowska M., Some nonsemisymmetric Ricci-semisymmetric warped product hy- persurfaces. Pulb Inst Math Beograd (N.S.). 72, 81-93.(2002).
  • Deszcz R., On pseudosymmetric spaces. Bull Soc Belg Math Ser A. 44, 1-34.(1992).
  • Deszcz R., Verstraelen L.,Yaprak S¸., Hypersurfaces with pseudosymmetric Weyl ten- sor in conformally flat manifolds. Geometry and Topology of Submanifolds IX. Valenci- ennes/Lyon/Leuven: World Scientific Publishing. 131-77 (1997).
  • Dabrowska M., Defever F., Deszcz R. and Kowalczyk D., Semisymmetry and Ricci- semisymmetry for hypersurfaces semi-Euclidean spaces. Publ. Inst. Math. (Beograd) (N.S.) 67, 103–111 (2000).
  • ¨Ozg¨ur C., Hypersurfaces satisfying some curvature conditions in the semi-Euclidean space. Chaos, Solitons and Fractals. 39, 2457-2464.(2009).
  • ¨Ozg¨ur, C., Arslan, K., On some class of hypersurfaces in En+1satisfying Chen’s equality. Turkish J. Math. 26, 283–293 (2002). [10] ¨Ozg¨ur, C., Arslan, K., Murathan, C., Conharmonically semi-parallel hypersurfaces. Proceed- ings of the Centennial ”G. Vranceanu”, Part II (Bucharest, 2000). An. Univ. Bucure¸sti Mat. Inform. 50, 121–132 (2001).
  • Prasad B., A pseudo projective curvature tensor on a Riemannian manifold, Bull. Calcutta Math. Soc. 94, 163-166 (2002).
  • Szabo ZI., Structure theorems on Riemannian spaces satisfying R(X, Y ) · R = 0. I. local version J. Diff. Geom. 17, 531-82 (1982).
  • Isiklar Air Force High School. Bursa-TURKEY
Year 2014, , 99 - 105, 01.06.2014
https://doi.org/10.36753/mathenot.207636

Abstract

References

  • Abdalla B.E., Dillen F.A., A Ricci-semi-symmetric hypersurface of Euclidean space which is not semi-symmetric. Proc Amer Math Soc. 130, 1805.(2002).
  • Defever F., Deszcz R., Dhooghe, P., Verstraelen L., Yaprak S¸., On Ricci-pseudosymmetric hypersurfaces in spaces of constant curvature. Results in Math. 27, 227-236 (1995).
  • Deszcz R., On certain classes of hypersurfaces in space of constant curvature. Geometry and Topology of Submanifolds VIII, World .Sci., Singapore. 101-110 (1996).
  • Deszcz R.,Glogowska M., Some nonsemisymmetric Ricci-semisymmetric warped product hy- persurfaces. Pulb Inst Math Beograd (N.S.). 72, 81-93.(2002).
  • Deszcz R., On pseudosymmetric spaces. Bull Soc Belg Math Ser A. 44, 1-34.(1992).
  • Deszcz R., Verstraelen L.,Yaprak S¸., Hypersurfaces with pseudosymmetric Weyl ten- sor in conformally flat manifolds. Geometry and Topology of Submanifolds IX. Valenci- ennes/Lyon/Leuven: World Scientific Publishing. 131-77 (1997).
  • Dabrowska M., Defever F., Deszcz R. and Kowalczyk D., Semisymmetry and Ricci- semisymmetry for hypersurfaces semi-Euclidean spaces. Publ. Inst. Math. (Beograd) (N.S.) 67, 103–111 (2000).
  • ¨Ozg¨ur C., Hypersurfaces satisfying some curvature conditions in the semi-Euclidean space. Chaos, Solitons and Fractals. 39, 2457-2464.(2009).
  • ¨Ozg¨ur, C., Arslan, K., On some class of hypersurfaces in En+1satisfying Chen’s equality. Turkish J. Math. 26, 283–293 (2002). [10] ¨Ozg¨ur, C., Arslan, K., Murathan, C., Conharmonically semi-parallel hypersurfaces. Proceed- ings of the Centennial ”G. Vranceanu”, Part II (Bucharest, 2000). An. Univ. Bucure¸sti Mat. Inform. 50, 121–132 (2001).
  • Prasad B., A pseudo projective curvature tensor on a Riemannian manifold, Bull. Calcutta Math. Soc. 94, 163-166 (2002).
  • Szabo ZI., Structure theorems on Riemannian spaces satisfying R(X, Y ) · R = 0. I. local version J. Diff. Geom. 17, 531-82 (1982).
  • Isiklar Air Force High School. Bursa-TURKEY
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

YUSUF Doğru This is me

Publication Date June 1, 2014
Submission Date March 9, 2015
Published in Issue Year 2014

Cite

APA Doğru, Y. (2014). HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE. Mathematical Sciences and Applications E-Notes, 2(1), 99-105. https://doi.org/10.36753/mathenot.207636
AMA Doğru Y. HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE. Math. Sci. Appl. E-Notes. June 2014;2(1):99-105. doi:10.36753/mathenot.207636
Chicago Doğru, YUSUF. “HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE”. Mathematical Sciences and Applications E-Notes 2, no. 1 (June 2014): 99-105. https://doi.org/10.36753/mathenot.207636.
EndNote Doğru Y (June 1, 2014) HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE. Mathematical Sciences and Applications E-Notes 2 1 99–105.
IEEE Y. Doğru, “HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE”, Math. Sci. Appl. E-Notes, vol. 2, no. 1, pp. 99–105, 2014, doi: 10.36753/mathenot.207636.
ISNAD Doğru, YUSUF. “HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE”. Mathematical Sciences and Applications E-Notes 2/1 (June 2014), 99-105. https://doi.org/10.36753/mathenot.207636.
JAMA Doğru Y. HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE. Math. Sci. Appl. E-Notes. 2014;2:99–105.
MLA Doğru, YUSUF. “HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE”. Mathematical Sciences and Applications E-Notes, vol. 2, no. 1, 2014, pp. 99-105, doi:10.36753/mathenot.207636.
Vancouver Doğru Y. HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE. Math. Sci. Appl. E-Notes. 2014;2(1):99-105.

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