Abstract:

We will consider a connection with totally skew-symmetric torsion on non-symmetric (semi-) Riemann manifolds that satisfy Einstein’s metric condition (EMC). We proved that an almost Hermitian manifold is a non-symmetric Riemann manifold that satisfies EMC if and only if it is a Nearly Kahler manifold. We will also show what happens in the case of para Hermitian manifold, contact, and para-contact manifolds that satisfy EMC. We show that a connection with skew symmetric torsion satisfying EMC exists on an almost contact metric manifolds when it is D-homothetic to a cosymplectic manifold. We proved the structure theorem for the new class of almost contact metric manifold and special attention we have focused on dimension 5. As a natural continuation of this research, we dealt with the case of Lorentzian manifolds.

This is joint work with Stefan Ivanov and Nikola Stanchev.