The equations of generalized complex structures on complex 2-tori.
The equations of structure of an -linear connection in the bundle of accelerations.
The equivariant Dehn's lemma and loop theorem.
The eta invariant and metrics of positive scalar curvature.
The Euclidean plane kinematics
Restricting his considerations to the Euclidean plane, the author shows a method leading to the solution of the equivalence problem for all Lie groups of motions. Further, he presents all transitive one-parametric system of motions in the Euclidean plane.
The Euler characteristic and signature for open manifolds
The Euler characteristic of vector fields on Banach manifolds and the problem of Plateau
The Euler theorem and Dupin indicatrix for surfaces at a constant distance from edge of regression on a surface in
The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids
This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either or or are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to , where is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...
The even Clifford structure of the fourth Severi variety
TheHermitian symmetric spaceM = EIII appears in the classification of complete simply connected Riemannian manifolds carrying a parallel even Clifford structure [19]. This means the existence of a real oriented Euclidean vector bundle E over it together with an algebra bundle morphism φ : Cl0(E) → End(TM) mapping Ʌ2E into skew-symmetric endomorphisms, and the existence of a metric connection on E compatible with φ. We give an explicit description of such a vector bundle E as a sub-bundle of End(TM)....
The evolution of harmonic mappings with free boundaries.
The evolution of the Dirac field in cuved space-times.
The evolution of the scalar curvature of a surface to a prescribed function
We investigate the gradient flow associated to the prescribed scalar curvature problem on compact riemannian surfaces. We prove the global existence and the convergence at infinity of this flow under sufficient conditions on the prescribed function, which we suppose just continuous. In particular, this gives a uniform approach to solve the prescribed scalar curvature problem for general compact surfaces.
The Evolution of the Weyl Tensor under the Ricci Flow
We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.
The Existence of Embedded Minimal Surfaces and the Problem of Uniqueness.
The existence of negatively Ricci curved metrics on three manifolds.
The Existence of Polarized F-structure on Volume Collapsed 4-manifolds.
The existence problem of hyperbolic structures on vector bundles.
The explicit construction of all harmonic two-spheres in G2 (Rn).
The explicit construction of Einstein Finsler metrics with non-constant flag curvature.