Isoparametric hypersurfaces in conic Finsler manifolds

Principal Curvatures of Isoparametric Hypersurfaces in Cp

Let M be an isoparametric hypersurface in CPn, and M the inverse image of M under the Hopf map. By using the relationship between the eigenvalues of the shape operators of M and M , we prove that M is homogeneous if and only if either g or l is constant, where g is the number of distinct principal curvatures of M and l is the number of non-horizontal eigenspaces of the shape operator on M .

Planar Normal Sections of Focal Manifolds of Isoparametric Hypersurfaces in Spheres

The present paper contains some results about the algebraic sets of planar normal sections associated to the focal manifolds of homogeneous isoparametric hypersurfaces in spheres. With the usual identification of the tangent spaces to the focal manifold with subspaces of the tangent spaces to the isoparametric hypersurface, it is proven that the algebraic set of planar normal sections of the fo...

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Homotheties of Finsler Manifolds *

We give a new and complete proof of the following theorem, discovered by Detlef Laugwitz: (forward) complete and connected finite dimensional Finsler manifolds admitting a proper homothety are Minkowski vector spaces. More precisely, we show that under these hypotheses the Finsler manifold is isometric to the tangent Minkowski vector space of the fixed point of the homothety via the exponential...