# Geometry Seminar – Kazuyuki Hasegawa

#### Event Details

Title: An inclusive immersion into a quaternion manifold and its invariants

Speaker: Kazuyuki Hasegawa (Kanazawa University)

Abstract: We introduce a quaternion invariant for an inclusive immersion in a quaternion manifold, which is a quaternion object corresponding to the Willmore functional. The lower bound of this invariant is given by topological one and the equality case can be characterized in terms of the natural twistor lift. When the ambient manifold is the quaternion projective space and the natural twistor lift is holomorphic, we obtain a relation between the quaternion invariant and the degree of the image of the natural twistor lift as an algebraic curve. Moreover the first variation formula for the invariant is obtained. As an application of the formula, if the natural twistor lift is a harmonic section, then the surface is a stationary point of the invariant under any variations such that the induced complex structures do not vary.

10 June 2016, 11:30, 1st floor Seminar room, IEMath-GR