Related papers: The Hermitian Connection and the Jacobi Fields of …

We give a new and complete proof of the following theorem, discovered by Detlef Laugwitz: (forward) complete and connected finite dimensional Finsler manifolds admitting a proper homothety are Minkowski vector spaces. More precisely, we…

A harmonic map from a Riemannian manifold into a Grassmannian manifold is characterized by a vector bundle, a space of sections of this bundle and a Laplace operator. We apply our main theorem, itself a generalization of a Theorem of…

We establish a stable homotopy-theoretic version of a recent result of Farber and Weinberger on the fibrewise topological complexity of sphere bundles and prove, by closely parallel methods, a similar result for real, complex and…

In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first…

Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of these formulas is obtained by exploiting some properties of…

A theorem by Mumford implies that every automorphic line bundle on a pure open Shimura variety, equipped with an invariant smooth metric, can be uniquely extended as a line bundle on a toroidal compactification of the variety, in such a way…

We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications,…

Motivated by the Hamilton$-$Jacobi approach of fields with constraints, we analyse the classical structure of three different constrained field systems: (i) the scalar field coupled to two flavors of fermions through Yukawa couplings (ii)…

An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate…

In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which…

Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.

We prove two results on geometric consequences of the representation of restricted holonomy group of a Hermitian connection. The first result concerns when such a Hermitian manifold is K\"ahler in terms of the torsion and the irreducibility…

We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…

We show that any two non-conjugate points on a forward or backward complete connected Finsler manifold can be joined by infinitely many geodesics which are not covered by finitely many closed ones, provided that the Betti numbers of the…

We generalize the property of Jacobi-orthogonality to indefinite scalar product spaces. We compare various principles and investigate relations between Osserman, Jacobi-dual, and Jacobi-orthogonal algebraic curvature tensors. We show that…

We give an introduction to (pseudo-)Finsler geometry and its connections. For most results we provide short and self contained proofs. Our study of the Berwald non-linear connection is framed into the theory of connections over general…

Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such…

We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…

Given a Kaehler manifold polarised by a holomorphic ample line bundle, we consider the circle bundle associated to the polarisation with the induced transversal holomorphic structure. The space of contact structures compatible with this…

We establish an integral formula on a smooth, precompact domain in a Kahler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula we prove an isoperimetric inequality in terms of a positive lower…