2012 Fiscal Year Final Research Report

An affine immersion from a manifold with certain structures on itstangent bundle and its application

Research Project

Project/Area Number	23740060
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Multi-year Fund
Research Field	Geometry
Research Institution	Tokyo University of Science
Principal Investigator	KUROSU Sanae 東京理科大学, 理学部, 理学部 (70457844)
Project Period (FY)	2011 – 2012
Keywords	微分幾何 / 部分多様体論
Research Abstract	１． We characterize an affine immersion from a manifold with almost product structure or an almost complex structure to a real affine space whose affine fundamental form is Hermitian or anti-Hermitian with the structure. As an application, we study an isometric immersion of a para-Kaehler manifold or an almost product Riemannian manifold, which is a manifold with metric which is compatible with the structures. Especially, we classify a para-pluriharmonic isometric immersion from a complete para-Kaehler manifold of codimension one or two. ２． We find a new construction of a tt*-bundle structure associated with a harmonic map from a Riemann surface into a sphere, that is a collaboration work with Katsuhiro Moriya. This construction is related to the Clifford algebra.

(4 results)