SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER METRIC ON A EIGHT-DIMENSIONAL MANIFOLDS

SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER...

Authors

  • Silas Longwap University of Jos
  • ABDOUL SALAM DIALLO U NIVERSIT É A LIOUNE D IOP DE B AMBEY UFR SATIC, D ÉPARTEMENT DE M ATH ÉMATIQUES B. P. 30, B AMBEY , S ÉN ÉGAL

Abstract

A pseudo-Riemannian manifold which admits a field of parallel
null r-planes, with r ≤ n 2 is a Walker n-manifold. A.G. Walker in [12] investi-
gated the canonical forms of the metrics and came out with some interesting re-
sults. Of special interest are the even-dimensional Walker manifolds (n = 2m)
with fields of parallel null planes of half dimension (r = m). In this paper, we
consider a perticular eight-dimensional Walker manifold, derive and investigate
some geometric properties of the curvature tensors of the Manifold. We give
some theorems for the metric to be Einstein and Locally Conformally Flat.

Author Biography

ABDOUL SALAM DIALLO, U NIVERSIT É A LIOUNE D IOP DE B AMBEY UFR SATIC, D ÉPARTEMENT DE M ATH ÉMATIQUES B. P. 30, B AMBEY , S ÉN ÉGAL

U NIVERSIT É A LIOUNE D IOP DE B AMBEY
UFR SATIC, D ÉPARTEMENT DE M ATH ÉMATIQUES
B. P. 30, B AMBEY , S ÉN ÉGAL

Ass. Prof

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Published

2022-12-27

How to Cite

Longwap, S., & SALAM DIALLO, A. (2022). SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER METRIC ON A EIGHT-DIMENSIONAL MANIFOLDS: SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER. Journal of the Nigerian Mathematical Society, 41(3), 223–234. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/873

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