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Year 2024, Volume: 16 Issue: 1, 272 - 284, 30.06.2024
https://doi.org/10.47000/tjmcs.1397889

Abstract

References

  • Abraham, R., Marsden, J.E., Ratiu, T., Manifolds, Tensor Analysis and Applications, Springer Verlag, New York Inc., 1998.
  • Barletta, E., Dragomir, S., Duggal, K. L., Lightlike Foliations of Semi-Riemannian Manifolds, American Mathematical Society, Providence, RI, 2007.
  • Bejancu, A., Duggal, K.L., Lightlike submanifolds of Semi- Riemannian manifolds, Acta Appl. Math., 38 (1995), 197–215.
  • Brickell, F., Clark, R.S., Differentiable Manifolds, Van Nostrand Reinhold Company London, 1970.
  • Duggal, K.L., Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  • Güneş, R., Şahin, B., Kılıç, E., On Lightlike hypersurfaces of a semi-Riemannian manifold, Turk J Math., 27(2003), 283–297.
  • Massamba, F., Lightlike hypersurfaces of indefinite Sasakian manifolds with parallel symmetric bilinear forms, Differential Geometry - Dynamical Systems, 10(2008), 226–234.
  • Sahin, B., Gunes, R., Lightlike real hypersurfaces of indefinet quaternion Kaehler manifolds, J. Geometry, 75(2002), 151–165.
  • Sakaki, M., On the definition of minimal lightlike submanifolds, International Electronic Journal of Geometry, 3(1)(2010), 16–23.
  • Tani, M., Prolongations of hypersurfaces to tangent bundles, Kodai Math. Sem. Rep., 21(1969), 85–96.
  • Yano, K., Ishihara S., Tangent and Cotangent Bundles, Marcel Dekker Inc., New York 1973.
  • Yano, K., Kobayashi, S., Prolongations of tensor fields and connections to tangent bundles I, General Theory, Jour. Math. Soc. Japan, 18(1966), 194–210.
  • Yıldırım, M., On level hypersurfaces of the complete lift of a submersion, An. Ş t. Univ. Ovidus Constanta, 17(2)(2009), 231–252.

On Level Hypersurfaces of the Vertical Lift of a Submersion

Year 2024, Volume: 16 Issue: 1, 272 - 284, 30.06.2024
https://doi.org/10.47000/tjmcs.1397889

Abstract

Suppose that $(M,G)$ be a Riemannian manifold and $f:M\rightarrow \mathbb{R}$ be a submersion. Then, the vertical lift of $f,$ $f^{v}:TM\rightarrow \mathbb{R}$ defined by $f^{v}=f\circ \pi $ is also a submersion. This interesting case, differently from [10], leads us to investigation of the level hypersurfaces of $f^{v}$ in tangent bundle $TM$. In this paper we obtained some differential geometric relations between level hypersurfaces of $f$ and $f^{v}.$ In addition, we noticed that, unlike [13], a level
hypersurface of $f^{v}$ is always lightlike, i.e., it doesn't depend on any additional condition.

References

  • Abraham, R., Marsden, J.E., Ratiu, T., Manifolds, Tensor Analysis and Applications, Springer Verlag, New York Inc., 1998.
  • Barletta, E., Dragomir, S., Duggal, K. L., Lightlike Foliations of Semi-Riemannian Manifolds, American Mathematical Society, Providence, RI, 2007.
  • Bejancu, A., Duggal, K.L., Lightlike submanifolds of Semi- Riemannian manifolds, Acta Appl. Math., 38 (1995), 197–215.
  • Brickell, F., Clark, R.S., Differentiable Manifolds, Van Nostrand Reinhold Company London, 1970.
  • Duggal, K.L., Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  • Güneş, R., Şahin, B., Kılıç, E., On Lightlike hypersurfaces of a semi-Riemannian manifold, Turk J Math., 27(2003), 283–297.
  • Massamba, F., Lightlike hypersurfaces of indefinite Sasakian manifolds with parallel symmetric bilinear forms, Differential Geometry - Dynamical Systems, 10(2008), 226–234.
  • Sahin, B., Gunes, R., Lightlike real hypersurfaces of indefinet quaternion Kaehler manifolds, J. Geometry, 75(2002), 151–165.
  • Sakaki, M., On the definition of minimal lightlike submanifolds, International Electronic Journal of Geometry, 3(1)(2010), 16–23.
  • Tani, M., Prolongations of hypersurfaces to tangent bundles, Kodai Math. Sem. Rep., 21(1969), 85–96.
  • Yano, K., Ishihara S., Tangent and Cotangent Bundles, Marcel Dekker Inc., New York 1973.
  • Yano, K., Kobayashi, S., Prolongations of tensor fields and connections to tangent bundles I, General Theory, Jour. Math. Soc. Japan, 18(1966), 194–210.
  • Yıldırım, M., On level hypersurfaces of the complete lift of a submersion, An. Ş t. Univ. Ovidus Constanta, 17(2)(2009), 231–252.
There are 13 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Articles
Authors

Mehmet Yıldırım 0000-0002-3578-6475

Ayşenur Özkan 0000-0002-9880-4060

Publication Date June 30, 2024
Submission Date November 29, 2023
Acceptance Date January 26, 2024
Published in Issue Year 2024 Volume: 16 Issue: 1

Cite

APA Yıldırım, M., & Özkan, A. (2024). On Level Hypersurfaces of the Vertical Lift of a Submersion. Turkish Journal of Mathematics and Computer Science, 16(1), 272-284. https://doi.org/10.47000/tjmcs.1397889
AMA Yıldırım M, Özkan A. On Level Hypersurfaces of the Vertical Lift of a Submersion. TJMCS. June 2024;16(1):272-284. doi:10.47000/tjmcs.1397889
Chicago Yıldırım, Mehmet, and Ayşenur Özkan. “On Level Hypersurfaces of the Vertical Lift of a Submersion”. Turkish Journal of Mathematics and Computer Science 16, no. 1 (June 2024): 272-84. https://doi.org/10.47000/tjmcs.1397889.
EndNote Yıldırım M, Özkan A (June 1, 2024) On Level Hypersurfaces of the Vertical Lift of a Submersion. Turkish Journal of Mathematics and Computer Science 16 1 272–284.
IEEE M. Yıldırım and A. Özkan, “On Level Hypersurfaces of the Vertical Lift of a Submersion”, TJMCS, vol. 16, no. 1, pp. 272–284, 2024, doi: 10.47000/tjmcs.1397889.
ISNAD Yıldırım, Mehmet - Özkan, Ayşenur. “On Level Hypersurfaces of the Vertical Lift of a Submersion”. Turkish Journal of Mathematics and Computer Science 16/1 (June 2024), 272-284. https://doi.org/10.47000/tjmcs.1397889.
JAMA Yıldırım M, Özkan A. On Level Hypersurfaces of the Vertical Lift of a Submersion. TJMCS. 2024;16:272–284.
MLA Yıldırım, Mehmet and Ayşenur Özkan. “On Level Hypersurfaces of the Vertical Lift of a Submersion”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 1, 2024, pp. 272-84, doi:10.47000/tjmcs.1397889.
Vancouver Yıldırım M, Özkan A. On Level Hypersurfaces of the Vertical Lift of a Submersion. TJMCS. 2024;16(1):272-84.