Abstract We study an action integral for Finsler gravity obtained by pulling back Einstein-Cartan-like Lagrangian from the tangent bundle to base manifold. The vacuum equations are imposing stationarity with respect any section (observer) and well posed as they independent of section. They imply that in metric is actually velocity variable so dynamics becomes coincident general relativity.

The Horrocks-Mumford bundle E is a famous stable complex vector bundle of rank 2 on 4-dimensional complex projective space. By construction, E has a natural Hermitian metric h1. On the other hand, stability implies the existence of a Hermitian-Einstein metric in E which is unique up to a positive scalar. Now the obvious question is if h1 is in fact the Hermitian-Einstein metric. In this note we...

Let (M, g) be an oriented 4-dimensional Riemannian manifold (not necessarily compact). Due to the Hodge-star operator ⋆, we have a decomposition of the bivector bundle ∧2 TM = ∧+ ⊕ ∧− . Here ∧± is the eigen-subbundle for the eigenvalue ±1 of ⋆. The metric g on M induces a metric, denoted by < , >, on the bundle ∧2 TM . Let π : Z = S (∧+) −→ M be the sphere bundle; the fiber over a point m ∈ M p...

This is the content of a talk given by the author at the 2009 Lehigh University Geometry/Topology Conference. Using the definition of connection given by Dieudonné, the Sasaki metric on the tangent bundle to a Riemannian manifold is expressed in a natural way. Also, the following property is established. The induced metric on the tangent bundle of an isometrically embedded submanifold is the Sa...

For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means fundamental tensor has Lorentzian signature on conic subbundle tangent bundle thus existence cone future-pointing time-like vectors is ensured. The identified (α,β)-Finsler spacetimes are candidates for applications i...

Given a proper, open, holomorphic map of Kahler manifolds, whose general fibers are Calabi-Yau the volume forms for Ricci-flat metrics induce hermitian metric on relative canonical bundle over regular locus family. We show that curvature form extends as closed positive current. Consequently Weil-Petersson In projective case, is known to be certain determinant line bundle, equipped with Quillen ...

given a pair (semispray $s$, metric $g$) on a tangent bundle, the family of nonlinear connections $n$ such that $g$ is recurrent with respect to $(s, n)$ with a fixed recurrent factor is determined by using the obata tensors. in particular, we obtain a characterization for a pair $(n, g)$ to be recurrent as well as for the triple $(s, stackrel{c}{n}, g)$ where $stackrel{c}{n}$ is the canonical ...

Examples of Kähler metrics of constant scalar curvature are relatively scarce. Over the past two decades, several workers in geometry and physics have used symmetry reduction to construct complete Kähler metrics of constant scalar curvature by ODE methods. One fruitful idea—the “Calabi ansatz”—is to begin with an Hermitian line bundle p : (L, h)→ (M, gM ) over a Kähler manifold, and to search f...

Using Fujita-Griffiths method of computing metrics on Hodge bundles, we show that for every semi-ample vector bundle E on a compact complex manifold, and every positive integer k, the vector bundle SE ⊗ detE has a continuous metric with Griffiths semi-positive curvature. If E is ample, the metric can be made smooth and Griffiths positive.

We deal with finite dimensional differentiable manifolds. All items are concerned with are differentiable as well. The class of differentiability is C∞. A metric structure in a vector bundle E is a constant rank symmetric bilinear vector bundle homomorphism of E × E in the trivial bundle line bundle. We address the question whether a given gauge structure in E is metric. That is the main concer...