Adopting the pullback formalism, a new linear connection in Finsler geometry has been introduced and investigated.
 Such unifies all formerly known connections some other not so far. Also, our is Finslerian version of Tripathi Riemannian geometry. The existence uniqueness such are proved intrinsically. An explicit intrinsic expression relating this to Cartan obtained. Some generalized cons...

We demonstrate that integrable abelian vortex equations on constant curvature Riemann surfaces can be reinterpreted as flat non-abelian Cartan connections. By lifting to three dimensional group manifolds we find higher analogues of vortices. These configurations are also encoded in a connection. give examples different types interpreted this way, and compare contrast representation with the sym...

LetG be a connected affine algebraic reductive group over C. Let P be a holomorphic principal G bundle on M (i.e. the transition functions of P are holomorphic). Assume that P admits a holomorphic connection D compatible with the holomorphic structure. This means the following : D is a holomorphic 1-form on P with values in the Lie algebra, g, of G, such that D is invariant for the action of G ...

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.

We define a conformally invariant action S on gauge connections closed pseudo-Riemannian manifold M of dimension 6. At leading order this is quadratic in the connection. The Euler-Lagrange equations S, with respect to variation connection, provide higher-order analogue (source-free) Yang-Mills equations. For any connection A M, we S(A) by first defining Lagrangian density associated A. This not...

We show that the extended principal bundle of a Cartan geometry type (A(m,R),GL(m,R)), endowed with its connection ωˆ, is isomorphic to A(m,R)-bundle affine frames as defined in classical Kobayashi-Nomizu volume I. Then we classify local holonomy groups canonically associated Riemannian manifold. It follows if group manifold compact then locally product cones.

Cartan’s spacetime reformulation of the Newtonian theory of gravity is a generallycovariant Galilean-relativistic limit-form of Einstein’s theory of gravity known as the Newton-Cartan theory. According to this theory, space is flat, time is absolute with instantaneous causal influences, and the degenerate ‘metric’ structure of spacetime remains fixed with two mutually orthogonal non-dynamical m...

We discuss the propagation of fermions on generic, curved branes in Ishibashi-Kawai-Kitazawa-Tsuchiya-type matrix models. The Dirac operator can be understood either terms a Weitzenb\"ock connection, or Levi-Civita connection with an extra torsion term. detail coupling spin to background geometry using Jeffreys-Wentzel-Kramers-Brillouin approximation. Despite absence local Lorentz invariance un...