Related papers: Diffeological Levi-Civita connections
In this historical note, we wish to highlight the crucial conceptual role played by the principle of virtual work of analytical mechanics, in working out the fundamental notion of parallel transport on a Riemannian manifold, which opened…
We investigate the relative logarithmic connections on a holomorphic vector bundle over a complex analytic family. We give a sufficient condition for the existence of a relative logarithmic connection on a holomorphic vector bundle singular…
A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of…
This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the…
We study the relations between the triviality of the tangent bundle $TM$ and the generalized tangent bundle $\mathbb{T}M = TM\oplus T^*M$ of a manifold. We show that the generalized tangent bundle of a paralellizable manifold is trivial. We…
Given a quotient vector bundle $\mathcal A$ over $X$ with kernel map $\kappa: X\to\mathrm{Max}\,A$ we study the codual bundle with fiber at each point $x\in X$ isomorphic to the dual of $\kappa(x)$. Applying the adjunction between quotient…
Consider a smooth manifold and an action on it of a compact connected Lie group with a bi-invariant metric. Then, any orbit is an embedded submanifold that is isometric to a normal homogeneous space for the group. In this paper, we…
It is given the diffeomorphism classification on generic singularities of tangent varieties to curves with arbitrary codimension in a projective space. The generic classifications are performed in terms of certain geometric structures and…
We complete the proof of the fact that the moduli space of rank two bundles with trivial determinant embeds into the linear system of divisors on $Pic^{g-1}C$ which are linearly equivalent to $2\Theta$. The embedded tangent space at a…
In this paper, we introduce a contact pseudo-metric structure on a tangent sphere bundle $T_\varepsilon M$. we prove that the tangent sphere bundle $T_{\varepsilon}M$ is $(\kappa, \mu)$-contact pseudo-metric manifold if and only if the…
In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and…
We give coordinate formula and geometric description of the curvature of the tensor product connection of linear connections on vector bundles with the same base manifold. We define the covariant differential of geometric fields of certain…
We investigate the concept of projective equivalence of connections in supergeometry. To this aim, we propose a definition for (super) geodesics on a supermanifold in which, as in the classical case, they are the projections of the integral…
We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation betwen them is described. A tangent structure is constructed for each pre-convenient…
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
In math.RT/0201073 we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) the category of constructible sheaves…
Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies…
We define an abstract notion of double Lie algebroid, which includes as particular cases: (1) the double Lie algebroid of a double Lie groupoid in the sense of the author, such as the iterated tangent bundle of an ordinary manifold, and…
We study the local differential geometry of varieties $X^n\subset \Bbb C\Bbb P^{n+a}$ with degenerate secant and tangential varieties. We show that the second fundamental form of a smooth variety with degenerate tangential variety is…
We study the link between a compact hypersurface in $\P^{n+1}$ and the set of all its tangent planes. In this context, we identify $\P^{n+1}$ to the set of linear subspaces of codimension one by orthogonal complementarity. This gives rise…