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The iterated version of a translative integral formula for sets of positive reach

Rataj, Jan (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

By taking into account the work of J. Rataj and M. Zähle [Geom. Dedicata 57, 259-283 (1995; Zbl 0844.53050)], R. Schneider and W. Weil [Math. Nachr. 129, 67-80 (1986; Zbl 0602.52003)], W. Weil [Math. Z. 205, 531-549 (1990; Zbl 0705.52006)], an integral formula is obtained here by using the technique of rectifiable currents.This is an iterated version of the principal kinematic formula for $q$ sets of positive reach and generalized curvature measures.

The Jacobi equation on naturally reductive compact Riemannian homogeneous spaces.

Wolfgang Ziller (1977)

Commentarii mathematici Helvetici

The Jacobi fields for a spray on the tangent bundle.

Bucataru, Ioan (1999)

Novi Sad Journal of Mathematics

The Jordan normal form of higher order Osserman algebraic curvature tensors

Peter Gilkey, Raina Ivanova (2002)

Commentationes Mathematicae Universitatis Carolinae

We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type $(r, s)$ in a vector space of signature $(p, q)$ . We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.

The kaehlerian structures and reproducing kernels

Anna Krok, Tomasz Mazur (1991)

Annales Polonici Mathematici

It is shown that one can define a Hilbert space structure over a kaehlerian manifold with global potential in a natural way.

The Kähler Ricci flow on Fano manifolds (I)

Xiuxiong Chen, Bing Wang (2012)

Journal of the European Mathematical Society

We study the evolution of pluri-anticanonical line bundles $K_{M}^{- ν}$ along the Kähler Ricci flow on a Fano manifold $M$ . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of $M$ . For example, the Kähler Ricci flow on $M$ converges when $M$ is a Fano surface satisfying $c_{1}^{2} (M) = 1$ or $c_{1}^{2} (M) = 3$ . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups....

The Killing Tensors on an $n$ -dimensional Manifold with $S L (n,)$ -structure

Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $S L (n,)$ -structure and discuss possible applications of obtained results in Riemannian geometry.

The Kuranishi space of complex parallelisable nilmanifolds

Sönke Rollenske (2011)

Journal of the European Mathematical Society

We show that the deformation space of complex parallelisable nilmanifolds can be described by polynomial equations but is almost never smooth. This is remarkable since these manifolds have trivial canonical bundle and are holomorphic symplectic in even dimension. We describe the Kuranishi space in detail in several examples and also analyse when small deformations remain complex parallelisable.

The $L^{2}$ metric in gauge theory: an introduction and some applications

David Groisser (1997)

Banach Center Publications

We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the $L^{2}$ metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.

The $L$ -dual of an $(α, β)$ Finsler space of order two.

Masca, Ioana Monica, Sabau, Vasile Sorin, Shimada, Hideo (2007)

Balkan Journal of Geometry and its Applications (BJGA)

The $L_{p q}$ -Cohomology of $S O L$

Vladimir Gol'dshtein, Marc Troyanov (1998)

Annales de la Faculté des sciences de Toulouse : Mathématiques

The L2-Structure of Moduli spaces of Einstein Metrics on 4-Manifolds.

M. Anderson (1992)

Geometric and functional analysis

The Lagrange rigid body motion

Tudor Ratiu, P. van Moerbeke (1982)

Annales de l'institut Fourier

We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of $s o (3) \times s o (3)$ ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group $S O (3) \times s o (3)$ with its natural...

The Laplace spectrum and Hermitian spaces.

Friedland, L. (2000)

Balkan Journal of Geometry and its Applications (BJGA)

The Laplace-Beltrami operator in almost-Riemannian Geometry

Ugo Boscain, Camille Laurent (2013)

Annales de l’institut Fourier

We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...

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