Antonio Martínez Naveira

On the Energy of Distributions, with Application to the Quaternionic Hopf Fibrations

Abstract. The energy of an oriented q-distribution ? in a compact oriented manifold M is defined to be the energy of the section of the Grassmannian manifold of oriented q-planes in M induced by ?. In the Grassmannian, the Sasaki metric is considered. We show here a condition for a distribution to be a critical point of the energy functional. In the spheres, we see that Hopf fibrations are critical points. Later, we prove the instability for these fibrations.

Geometry of extended Bianchi–Cartan–Vranceanu spaces

The differential geometry of three-dimensional Bianchi, Cartan and Vranceanu (BCV) spaces is well known. We introduce the extended Bianchi, Cartan and Vranceanu (EBCV) spaces as a natural seven dimensional generalization of BCV spaces and study some of their main geometric properties, such as the Levi-Civita connection, Ricci curvatures, Killing fields and geodesics.

VARIATIONAL PROPERTIES OF THE INTEGRATED MEAN CURVATURES OF TUBES IN SYMMETRIC SPACES

Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of Pt and their derivatives with respect to t. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.

Total curvatures of compact complex submanifolds in\(C/P^n\)

AbstractLetM be a complex submanifold in

CORRECTED ENERGY OF DISTRIBUTIONS ON RIEMANNIAN MANIFOLDS

C/P^n

A method for the resolution of the Jacobi equation Y″ + RY = 0 on the manifold Sp(2)/SU(2)

. We define the total curvatures ofM and we get a local interpretation of them. Finally, we give a topological characterization for the total (non-absolute) curvature of complex hypersurfaces in

Volume of tubes in noncompact symmetric spaces

C/P^n