相关论文: A General Expression for the Quartic Lovelock Tens…
The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…
We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of the linear group GL(n) representations and universal upper bounds on the relative dimensions of irreducible components of a tensor…
In this paper we consider the general structure of irreducible tensor representations of the Poincare group of arbitrary dimension with multiple sets of Lorentz indices and different ways to construct them from basic elements (Lorentz…
The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown…
We study the Riemann curvature tensor of (\kappa,\mu,\nu)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and…
We relate certain universal curvature identities for Kaehler manifolds to the Euler-Lagrange equations of the scalar invariants which are defined by pairing characteristic forms with powers of the Kaehler form.
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
A higher order theory of dilaton gravity is constructed as a generalization of the Einstein-Lovelock theory of pure gravity. Its Lagrangian contains terms with higher powers of the Riemann tensor and of the first two derivatives of the…
It is well known that the Jacobi operators completely determine the curvature tensor. The question of existence of a curvature tensor for given Jacobi operators naturally arises, which is considered and solved in the previous work.…
A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
Robertson-Walker and Generalized Robertson-Walker spacetimes may be characterized by the existence of a time-like unit torse-forming vector field, with other constrains. We show that Twisted manifolds may still be characterized by the…
It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of…
We study the properties of LP-Sasakian manifolds endowed with generalized $% \eta -$Ricci solitons associated to the general connection. Finally, the existence of such solitons on a 4-dimensional LP-Sasakian manifold is proved by…
Given a (semi-Riemannian) generalised metric $\mathcal G$ and a divergence operator $\mathrm{div}$ on an exact Courant algebroid $E$, we geometrically construct a canonical generalised Levi-Civita connection $D^{\mathcal G, \mathrm{div}}$…
Some general Finsler connections are defined. Emphasis is being made on the Cartan tensor and its derivatives. Vanishing of the hv-curvature tensors of these connections characterizes Landsbergian, Berwaldian as well as Riemannian…
Solutions to the $n$-dimensional Laplace equation which are constant on a central quadric are found. The associated twistor description of the case $n=3$ is used to characterise Gibbons-Hawking metrics with tri-holomorphic $SL(2, \C)$…
The "positive square" of any tensor is presented in a universal and unified manner, valid in Lorentzian manifolds of arbitrary dimension, and independently of any (anti)-symmetry properties of the tensor. For rank-m tensors, the positive…
We generalize the Stueckelberg formalism in the (1/2,1/2) representation of the Lorentz Group. Some relations to other modern-physics models are found.
Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…