IJPAM: Volume 47, No. 3 (2008)


Vishnu V. Reddy$^1$, Ramesh Sharma$^2$, S. Sivaramakrishnan$^3$
$^{1,3}$Department of Physics
Sri Sathya Sai University
Prasanthinilayam, 515134, INDIA
$^1$e-mail: einstein.vishnu@gmail.com
$^3$e-mail: sivaram@gmail.com
$^2$Department of Mathematics
University Of New Haven
300, Boston Post Road, West Haven, CT 06516, USA
e-mail: rsharma@newhaven.edu

Abstract.In this paper we consider Lorentzian metric induced from a Riemannian metric by a unit vector field. First we show that the Levi-Cita connections of the two metrics are equal if and only if the vector field is parallel. Next we examine the conformal vector fields and Jacobi vector fields for those metrics. Finally, we assume that the vector field is the Reeb vector field of a $K$-contact manifold and show that if a vector field is conformal with respect to both metrics, then it is Killing.

Received: March 18, 2008

AMS Subject Classification: 53B30, 83C15, 53D10

Key Words and Phrases: Lorentzian metric, Riemannian metric, Levi-Cita connections, parallel vector field, Reeb vector field

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 3