ON SEMI-DECOMPOSABLE PSEUDO-SYMMETRIC WEYL SPACES

Abstract

In this paper, we first prove that, if a semi-decomposable Weyl , space W_n can be written as the product of two Weyl spaces W_q and W^*_n-q then W_n has homothetic metrics. Next, after having given the definitions of symmetric and pseudo-symmetric Weyl spaces, we have shown that the symmetric Weyl space W_n can be written as the product of the symmetric subspaces W_q and W^*_n-q if and only if the complementary vector field of W_q is the gradient of $\ln\sqrt{\sigma}$. Finally, we prove two theorems concerning semi-decomposable pseudo-symmetric Weyl spaces.