Kähler immersions of Kähler–Ricci solitons into definite or indefinite complex space forms

Minimal Lagrangian isotropic immersions in indefinite 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...

Isotropic Lagrangian Submanifolds in Complex Space Forms

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

On Definite Quadratic Forms, Which Are Not the Sum of Two Definite or Semi-definite Forms

be a positive definite quadratic form with determinant D R and integer coefficients a ;Call it an even form if all a ; ; are even ., an odd form if at least one a ;; is odd . Then Í,, is called non-decomposable, if it cannot be expressed as a sum of two non-negative quadratic forms with integer coefficients . Mordell 1 ) proved that f, can always be decomposed into a sum of five squares of line...

Curved Flats, Pluriharmonic Maps and Constant Curvature Immersions into Pseudo-riemannian Space Forms

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences between global isometric immersion problems among different space forms and pseudoRiemannian space forms. As a corollary, we obtain a non-immersibili...