Tensor product of planer curves and space curves


Thesis Type: Postgraduate

Institution Of The Thesis: Uludağ Üniversitesi, Turkey

Approval Date: 2004

Thesis Language: Turkish

Student: REFİKA YÜCEL

Supervisor: CENGİZHAN MURATHAN

Abstract:

The object of this is to study tensor product surfaces of two curves. The thesis has three chapters. First chapter is the summary of the thesis. In the first chapter, we introduce basic concepts such as; vector space, isometric immersion, Laplacian operator, Riemannian manifold, shape operator, second fundamental form, tensor product, tensor space transversal immersion. In the final chapter we consider tensor product surface of two plane curves and we give necessary and sufficient conditions for such surfaces to be minimal[MVVW]. Secondly we consider tensor product surfaces of two Lorentzian plane curves we give necessary and sufficient conditions for the surface to be become minimal. Finally we consider tensor product surface of a space curve with a plane curve. And we give necessary and sufficient conditions for such surfaces to be minimal.