The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on September 09, 2014 at 14:00 in Room 478 of IMI.

A talk on:

„Surfaces in Euclidean Space Eⁿ⁺²”

will be delivered by Prof. Kadri Arslan from Uludağ University, Bursa, Turkey.

Everybody is invited.

Abstract.

In the present study we consider basic important concepts of differential geometry of surfaces in Eⁿ⁺², particularly including tangential and normal spaces along with the concept of orthonormal normal frames and orthogonal transformations between them. Furthermore, we define the three fundamental forms, Gauss equations and Weingarten equations. Finally we concentrate on curvature properties of the surfaces in Eⁿ⁺². In the second part we derive the integrability conditions of Codazzi-Mainardi, Ricci and the theorema egregium from the equations of Gauss and Weingarten. In particular, we introduce the Riemannian curvature tensor and the curvature tensor of the normal bundle. Further, we give some examples on 4-dimensional Euclidean space E⁴.

References:

[1] B. Y. Chen, Geometry of Submanifols, Dekker, New York (1973).
[2] Yu. Aminov, The Geometry of Submanifolds. Gordon and Breach Science Publishers, Singapore, 2001.
[3] B. Bulca and K. Arslan, Surfaces Given with the Monge Patch in E4: J. Math. Physics, Analysis, Geometry 05/2013.