Поредното заседание на Общия семинар на секция "Анализ, геометрия и топология" ще се проведе на 9 септември 2014 г. от 14:00 часа в зала 478 на ИМИ.

Доклад на тема:

„Surfaces in Euclidean Space Eⁿ⁺²”

ще изнесе prof. Kadri Arslan, Uludağ University, Bursa, Turkey.

Поканват се всички интересуващи се.

Резюме:

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.