Ισομετρικές εμβαπτίσεις πολυπτυγμάτων Kaehler (Master thesis)

Κασιούμης, Θεόδωρος


One of the basic problems in the theory of isometric immersions, is to decide if a given isometric immersion f : M → N is the unique way to isometrically immerse the Riemannian manifold M into the Riemannian manifold N , up to an isometry of N . If this is the case, then f is called rigid. When f is not rigid, it is very important to find nontrivial isometric deformations of f . In this thesis we will prove that any minimal isometric immersion f : Mn → Qn+p of a simply connected Kaehler manifold Mn into a space of constant sectional curva- ture Qn+p, admits a 1-parameter associated family of minimal isometric immersions, up to congruence. We will conclude that the associated family is trivial if and only is f is pseudohomlomorphic. Furthermore, in Euclidean spaces we will deduce that every minimal immersion of a Kaehler manifold is pluriminimal, that every holomorphic isometric immersion is minimal and any pluriminimal isometric immersion admits a unique holomorphic representative. In the final chapter we will present the Gauss Parametrization of an Euclidean hypersurface whose nullity is of codimension two (no flat points). Then we use this tool in order to give a complete classification of Kaehler hypersurfaces into Euclidean spaces with no flat points.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών
Subject classification: Γεωμετρία, Διαφορική
Keywords: Γεωμετρία,Πολυπτύγματα Kaehler,Ισομετρικές εμβαπτίσεις
URI: http://olympias.lib.uoi.gr/jspui/handle/123456789/28017
Appears in Collections:Διατριβές Μεταπτυχιακής Έρευνας (Masters)

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