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 introduce semi-symmetric metric Koszul forms and non-metric on singular semi-Riemannian manifolds. Semi-symmetric their curvature of semi-regular warped products are expressed in terms those the factor We also associated to almost product structure Furthermore, generalize results \cite{St2} multiply products.

This research deals with the generalized symmetric metric U-connection defined on golden Lorentzian manifolds. We also derive sharp geometric inequalities that involve normalized δ-Casorati curvatures for submanifolds of manifolds equipped U-connection.

We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical antiinvariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quartersymmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions ...

We classify 7-dimensional cocalibrated G2-manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection ∇ with totally skew-symmetric torsion and a spinor field Ψ1 solving the equations in the common sector of type II superstring theory. There exist G2-structures with parallel characteristic torsion that are not naturally reductive. 1. Metri...