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THE BOCHNER VANISHING THEOREMS ON THE CONFORMAL KILLING VECTOR FIELDS

Year 2019, Volume: 9 Issue: 1, 114 - 120, 01.03.2019

S. Eker

Abstract

In this paper, the result of the Bochner vanishing theorems, indicating the conditions that every conformal killing vector elds is parallel and there is no nontrivial Conformal Killing vector eld, are satis ed under two di erent modi cated Ricci tensors.

Keywords

Ricci curvature Conformal Killing vector eld Vanishing theorem Bochner technique.

References

  • Bochner, S., (1946), Vector fields and Ricci curvature. Bull. Amer. Math. Soc. 52, 776-797.
  • Bochner, S. and Yano K., (1953), Curvature and Betti numbers, Ann. of Math. Stud., no. 32, Princeton Univ. Press.
  • Deshmukh, S., Al-Solamy FR., (2014), Conformal vector fields on a Riemannian manifold, Balkan J. Geom. Appl. 19, 86-93.
  • Jost, J., (2002), Riemannian Geometry and Geometric Analysis, Berlin, Germany: Springer-Verlag.
  • Kashiwada, T., (1968), On conformal Killing tensor, Natur. Sci. Rep. Ochanomizu Univ. 19, 67-74.
  • Kodaira, K., (1953), On a differential-geometric method in the theory of analytic stacks, Proc. Natl. Acad. Sci. USA 39, 1268-1273.
  • Lichnerowicz, A., (1958), Geometries des groupes de transformations, Paris, France: Dunod.
  • Lichnerowicz, A., (1948), Courboure et nombres de Betti dune variete riemannienne compacts, C.R. Acad. Sci. Paris 226, 1678-1680.
  • Lott, J., (2003), Some geometric properties of the Bakry- Emery- Ricci Tensor, Comment. Math. Helv. 78, 865-883.
  • Mogi, I., (1950), On harmonic field in Riemannian manifold, Kodai Math. Sem. Rep. 2, 61-66.
  • Tomonaga, Y., (1950), On Betti numbers of Riemannian spaces, J. Math. Soc. Japan 2, 93-104.
  • Murat, L., (2009), The Bochner technique and modification of the Ricci Tensor, Ann. Global Anal. Geom. 36, 285-291.
  • Petersen, P., (1998), Riemannian Geometry, New York, USA: Springer-Verlag.
  • Wei, G. and Wylie, W., (2009), Comparison geometry for the Bakry-Emery-Ricci tensor, J. Differential Geom. 83, 337-405.
  • Yano, K., (1952), On harmonic and Killing vector fields, Ann. of Math. 55, 38-45.

Year 2019, Volume: 9 Issue: 1, 114 - 120, 01.03.2019

S. Eker

Abstract

References

  • Bochner, S., (1946), Vector fields and Ricci curvature. Bull. Amer. Math. Soc. 52, 776-797.
  • Bochner, S. and Yano K., (1953), Curvature and Betti numbers, Ann. of Math. Stud., no. 32, Princeton Univ. Press.
  • Deshmukh, S., Al-Solamy FR., (2014), Conformal vector fields on a Riemannian manifold, Balkan J. Geom. Appl. 19, 86-93.
  • Jost, J., (2002), Riemannian Geometry and Geometric Analysis, Berlin, Germany: Springer-Verlag.
  • Kashiwada, T., (1968), On conformal Killing tensor, Natur. Sci. Rep. Ochanomizu Univ. 19, 67-74.
  • Kodaira, K., (1953), On a differential-geometric method in the theory of analytic stacks, Proc. Natl. Acad. Sci. USA 39, 1268-1273.
  • Lichnerowicz, A., (1958), Geometries des groupes de transformations, Paris, France: Dunod.
  • Lichnerowicz, A., (1948), Courboure et nombres de Betti dune variete riemannienne compacts, C.R. Acad. Sci. Paris 226, 1678-1680.
  • Lott, J., (2003), Some geometric properties of the Bakry- Emery- Ricci Tensor, Comment. Math. Helv. 78, 865-883.
  • Mogi, I., (1950), On harmonic field in Riemannian manifold, Kodai Math. Sem. Rep. 2, 61-66.
  • Tomonaga, Y., (1950), On Betti numbers of Riemannian spaces, J. Math. Soc. Japan 2, 93-104.
  • Murat, L., (2009), The Bochner technique and modification of the Ricci Tensor, Ann. Global Anal. Geom. 36, 285-291.
  • Petersen, P., (1998), Riemannian Geometry, New York, USA: Springer-Verlag.
  • Wei, G. and Wylie, W., (2009), Comparison geometry for the Bakry-Emery-Ricci tensor, J. Differential Geom. 83, 337-405.
  • Yano, K., (1952), On harmonic and Killing vector fields, Ann. of Math. 55, 38-45.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

S. Eker This is me

Publication Date March 1, 2019
Published in Issue Year 2019 Volume: 9 Issue: 1

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