Abstract We continue our study of the mixed Einstein–Hilbert action as a functional pseudo-Riemannian metric and linear connection. Its geometrical part is total scalar curvature on smooth manifold endowed with distribution or foliation. develop variational formulas for quantities extrinsic geometry metric-affine space use them to derive Euler–Lagrange equations (which in case space-time are an...

In this paper we establish a direct connection between stable approximate unitary equivalence for ∗-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity assumptions. To this purpose we show that a topology on the Kasparov groups can be defined in terms of approximate unitary equivalence for Cuntz pairs and that this to...

The series-parallel (SP) graphs are those containing no topological K 4 and are considered trivial. We relax the prohibition distinguishing the SP graphs by forbidding only embeddings of K4 whose edges with both ends 3-valent (skeleton hereafter) induce a graph isomorphic to certain prescribed subgraphs of K 4 . In particular, we describe the structure of the graphs containing no embedding of K...

The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that structure a para-Kähler-like manifold constant curvature in Kurose's sense Hessian structure. also derive properties submersions which are compatible results illustrated by several nontrivial examples.