Totally real minimal immersions of $n$-dimensional real space forms into $n$-dimensional complex space forms

Spherical Minimal Immersions of Spherical Space Forms

Introduction. A number of authors [C], [DW1], [DW2], [L], [T] have studied minimal isometric immersions of Riemannian manifolds into round spheres, and in particular of round spheres into round spheres. As was observed by T. Takahashi [T], if Φ:M → S(r) ⊂ R is such a minimal immersion, then the components of Φ must be eigenfuctions of the Laplace operator on M for the same eigenvalue. And conve...

Minimal Lagrangian isotropic immersions in indefinite complex space forms

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essent...

SPECIAL n-FORMS ON A 2n-DIMENSIONAL VECTOR SPACE

The configuration of regular 3-forms in dimension 6 is generalized to n-forms in dimension 2n. The algebras of complex, paracomplex, and dual numbers are systematically used. The automorphism groups of all forms are determined. In the last decade there has arisen interest in exterior forms of higher degree, first of all in forms of degree 3 (see [2] and [3]). It is known (see [4] and [1]) that ...

Real Hypersurfaces with Constant Totally Real Bisectional Curvature in Complex Space Forms

In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space formMm(c), c 6= 0 as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional curvature given in [11].