On a Pair of Connections on a Principal Fibre Bundle
We prove that every generalized Cartan hypersurface satisfies the so called Roter type equation. Using this fact, we construct a particular class of generalized Robertson-Walker spacetimes.
We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field belonging to the -nullity distribution and -nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with belonging to - and -nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with belonging to -nullity distribution...
The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.