Invited Speaker
Assoc. Prof. Miroslava Antić
Faculty of Mathematics, University of Belgrade, SerbiaSpeech Title: A special Construction of Lagrangian Submanifolds in a Flat Complex Space
Abstract: Lagrangian submanifolds play an important role in classical mechanics and mathematical physics in particular in supersymmetric field theories and in string theory. Hence their structure and particular types of examples are subject of great interest.
The procedure of constructing a Lagrangian immersion in the complex projective space, starting with two other Lagrangian immersions into complex projective spaces of lesser dimension is known as a Calabi product, motivated by the similar construction in the affine differential geometry. In particular, one may consider a point instead of the one of the immersions, and in both cases the submanifold has a warped product structure of the interval and one or two Lagrangian immersions. Such Lagrangian submanifold then admits a splitting of the tangent bundle into orthogonal subbundles defined in terms of the corresponding second fundamental form, in case of a point and an immersion decomposition consists of two components and in case of a proper Calabi product, decomposition has three components. The generalization of this notion was investigated for Lagrangian immersions in non-flat complex space forms. Here we study the flat case and investigate the properties of the Lagrangian immersions with tangent bundle admitting the decomposition in question and we give explicit expressions for such immersions.