International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 4, Pages 727-736
Some invariant theorems on geometry of Einstein non-symmetric field theory
1Institute of Mathematics, The Academy of Sciences of China, China
2Department of Mathematics, University of Science and Technology of China, China
3Department of Mathematics, Princeton University, 08544, New Jersey, USA
Received 30 August 1982
Copyright © 1983 Liu Shu-Lin and Xu Sen-Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper generalizes Einstein's theorem. It is shown that under the
curvature tensor , Ricci tensor , and scalar curvature are all invariant, where is a closed -differential form on an -dimensional manifold .
It is still shown that for arbitrary , the transformation that makes curvature tensor (or Ricci tensor ) invariant
must be transformation, where (its components are ) is a second order differentiable covariant tensor field with vector value.