arXiv subjects

Mihai Anastasiei

Publications and source records attributed to Mihai Anastasiei.

7 recordsLinked to original sources

arXiv2014

Some remarks on Myers theorem for Finsler manifolds

The standard Bonnet-Myers theorem says that if the Ricci scalar of a Riemannian manifold is bounded below by a positive number, then the manifold is compact. Moreover, a bound of its diameter is pointed out. The theorem was extended to Finsler manifolds. In this paper we prove that if a certain condition on the average of the Ricci scalar holds, then the Finsler manifold M is compact if the Ricci scalar is bounded above by the same positive number. An upper bound of the diameter is also found. With no condition on Ricci scalar itself but with a different one on its average, we find that the Finsler manifold M is again compact. This time no bound of the diameter is found.The proofs are given in the Finslerian setting and are based on the index form along geodesics.

math.DG↗

arXiv2013

A compactness theorem in Finsler geometry

Let (M.F) be a complete Finsler manifold and P be a minimal and compact submanifold of M. Ric_k(x), x in M is a differential invariant that interpolates between the flag curvature and the Ricci curvature. We prove that if on any geodesic c(t) emanating orthogonally from P we have \int_{0}^{\infty}\mathbf{Ric}_{k}(t)>0, then M is compact.

math.DG↗

arXiv2012

Selected papers

Before retiring, looking back to forty years of writing and publishing scientific papers, I decided to present to the scientific community a selection of my scientific works. I chose mostly articles published in prestigious journals or Proceedings that made a certain impact in the scientific world. I have selected thirty two out of some ninety papers, on the following subjects :Geometry of conformal and spin structures on Hilbert manifolds,Geometry of tangent bundle of a Finsler or a Lagrange manifold,Applications of techniques from Finsler geometry to Mechanics and Physics, Geometry of total space of a vector bundle, Applications of Lie algebroids to Mechanics

math.DG↗

arXiv2010

Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo-Finsler/ Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions with regular rotating event horizon. For corresponding parameterizations, the metrics and connections define Finsler-Einstein geometries modeled on tangent bundles, or on nonholonomic (pseudo) Riemannian manifolds. In general, there are vacuum nonholonomic gravitational configurations which can not be generated in the limit of zero cosmological constant.

hep-th↗

arXiv2010

Metrizable linear connections in a Lie algebroid

A linear connection $D$ in a Lie algebroid is said to be metrizable if there exists a Riemannian metric $h$ in the Lie algebroid such that $Dh=0$. Conditions for the linear connection $D$ to be metrizable are investigated.

math.DG↗

arXiv2010

Banach Lie algebroids

First, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

math.DG↗

arXiv2008

Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles

We provide a method of converting Lagrange and Finsler spaces and their Legendre transforms to Hamilton and Cartan spaces into almost Kaehler structures on tangent and cotangent bundles. In particular cases, the Hamilton spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on effective phase spaces. This allows us to define the corresponding Fedosov operators and develop deformation quantization schemes for nonlinear mechanical and gravity models on Lagrange- and Hamilton-Fedosov manifolds.

math-ph↗