Theory of General Relativity is considered from the point of view of its general structure; it has been showed that if one assumes any connection to be a metric connection then Cartan tensor must necessary be completely antisymmetric, and an example of application is considered in the case of Lie group theory. Under a geometrical point of view, Cartan tensor is thought to represent the Torsion ...

We study massless Duffin-Kemmer-Petiau (DKP) fields in the context of Einstein-Cartan gravitation theory. In the case of an identically vanishing torsion (Riemannian space-times) we show that there exists local gauge symmetries which reproduce the usual gauge symmetries for the massless scalar and electromagnetic fields. On the other hand, similarly to what happens with the Maxwell theory, a no...

Motivated by recent developments on visible actions on complex manifolds, we raise a question whether or not the multiplication of three subgroups L, G and H surjects a Lie group G in the setting that G/H carries a complex structure and contains G/G ∩ H as a totally real submanifold. Particularly important cases are when G/L and G/H are generalized flag varieties, and we classify pairs of Levi ...

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...

We perform a covariant $1+3$ split of the Newton-Cartan equations. The resulting 3-dimensional system equations, called $1+3$-Newton-Cartan is structurally equivalent to $1+3$-Einstein In particular it features momentum constraint, and choice adapted coordinates corresponds shift vector. show that these equations reduce classical Newton without need for special Galilean coordinates. solutions a...