The generalized Lichnerowicz formula and analysis of Dirac operators.
The generalized regular functions over conformal quaternionic manifold
The generic dimension of the first derived system
Any -dimensional subbundle of the cotangent bundle on an -dimensional manifold partitions into subsets ( being the minimum of and , the combinations of things taken 2 at a time). is the set on which the first derived systems of the subbundle has codimension .In this paper we prove the following:Theorem. Let and let be a generic -dimensional subbundle...
The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds
The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions
In a previous note the author gave a generalisation of Witten’s proof of the Morse inequalities to the model of a complex singular curve and a stratified Morse function . In this note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of .
The geometry and spectrum of the one holed torus.
The geometry of a closed form
It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.
The Geometry of Critical and Near-Critical Values of Differentiable Mappings.
The geometry of Kato Grassmannians
We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.
The geometry of Markov diffusion generators
The geometry of pseudo harmonic morphisms.
The geometry of Teichmüller space via geodesic currents.
The geometry of the moduli space of CP2 instantons.
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
The global Yang-Mills equations depending on an arbitrary metric
The globally homeomorphic solutions to Beltrami system in Cn.
The Gluck and Ziller problem with the euclidean metric
The graded differential geometry of mixed symmetry tensors
We show how the theory of -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.
The graded representations of an affine Lie algebra
The gradient flow of Higgs pairs
We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle over a Kähler surface , and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point of this functional. We also prove that the limiting Higgs pair can be extended smoothly to a vector bundle over...