Taiwanese Journal of Mathematics

On the Second Equation of Obata

Fazilet Erkekoglu

Full-text: Open access


In this paper we prove some results related to a certain vector field satisfying the second equation of Obata [8] on vector fields.

Article information

Taiwanese J. Math., Volume 15, Number 2 (2011), 773-786.

First available in Project Euclid: 18 July 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C99: None of the above, but in this section 58J99: None of the above, but in this section

second covariant differential divergence Laplacian conformal vector field affine conformal vector field k-nullity vector field projective vector field Möbius equation


Erkekoglu, Fazilet. On the Second Equation of Obata. Taiwanese J. Math. 15 (2011), no. 2, 773--786. doi:10.11650/twjm/1500406234. https://projecteuclid.org/euclid.twjm/1500406234

Export citation


  • Y. H. Clifton and R. Maltz, The k-Nullity Space of Curvature Operator, Michigan Math. J., 17 (1970), 85-89.
  • F. Erkeko\u glu, On Special Cases of Local Möbius Equations, Publ. Math. Debrecen, Tomus, 67 (2005), Fasc. 1-2, 155-167.
  • F. Erkeko\u glu, E. Garcia-Rio, D. N. Kupeli and B. \" Unal, Characterizing Specific Riemannian Manifolds By Differential Equations, Acta Applicandae Mathematicae, 76(2) (2003) 195-219.
  • F. Erkeko\u glu, D. N. Kupeli and B. \" Unal, Some Results Related to the Laplacian on Vector Fields, Publ. Math. Debrecen, Tomus, 69 (2006), Fasc. 1-2, 137-154.
  • D. Ferus, Totally Geodesic Foliations, Math. Ann., 188 (1970), 313-316.
  • E. Garcia-Rio, D. N. Kupeli and B. \" Unal, On a Differential Equation Characterizing Euclidean Sphere, Journal of Differential Equations, 194 (2003) 287-299.
  • T. Nagano, The Projective Transformation with a Parallel Ricci Tensor, dai Math. Sem. Rep., 11 (1959), 131-138.
  • M. Obata, Riemannian Manifolds Admitting a Solution of a Certain System of Equations, Proc. United States-Japan Seminar in Differential Geometry, Kyoto, (1965), 101-114.
  • W. A. Poor, Differential Geometric Structures, McGraw-Hill, New York, 1981.
  • S. Tanno, Some Differential Equations on Riemannian Manifolds, J. Math. Soc. Japan, 30(3) (1978), 509-531.
  • K. Yano, Integral Formulas in Riemannian Geometry, Marcel Dekker, New York, 1970.