On a generalized Calabi-Yau equation
Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-Kähler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension .
On contact equivalence of holomorphic Monge-Ampére equations.
On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles
In this short survey, we would like to overview the recent development of the study on Deligne-Malgrange lattices and resolution of turning points for algebraic meromorphic flat bundles. We also explain their relation with wild harmonic bundles. The author hopes that it would be helpful for access to his work on wild harmonic bundles.
On -natural conformal vector fields on unit tangent bundles
We study conformal and Killing vector fields on the unit tangent bundle, over a Riemannian manifold, equipped with an arbitrary pseudo-Riemannian -natural metric. We characterize the conformal and Killing conditions for classical lifts of vector fields and we give a full classification of conformal fiber-preserving vector fields on the unit tangent bundle endowed with an arbitrary pseudo-Riemannian Kaluza-Klein type metric.
On higher order geometry on anchored vector bundles
Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.
On left invariant CR structures on
There is a well known one–parameter family of left invariant CR structures on . We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.
On natural metrics on tangent bundles of Riemannian manifolds
There is a class of metrics on the tangent bundle of a Riemannian manifold (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric [Kow-Sek1]. We call them “-natural metrics" on . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on from some quadratic forms on to find metrics (not necessary Riemannian)...
On projectable objects on fibred manifolds
The aim of this paper is to study the projectable and -projectable objects (tensors, derivations and linear connections) on the total space of a fibred manifold , where is a normalization of .
On Riemannian geometry of tangent sphere bundles with arbitrary constant radius
We shall survey our work on Riemannian geometry of tangent sphere bundles with arbitrary constant radius done since the year 2000.
On the completeness of total spaces of horizontally conformal submersions
In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class...
On the determinant of Gauss-Manin connections and hypergeometric functions of hypersurfaces.
On the geometry of free loop spaces.
On the principal bundles over a flag manifold.
On the torsion of spaces with connection
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface (II).
In [6], orbifold G-bundles on a certain class of elliptic fibrations over a smooth complex projective curve X were related to parabolic G-bundles over X. In this continuation of [6] we define and investigate holomorphic connections on an orbifold G-bundle over an elliptic fibration.