Differential geometry of curves

Chapter 2

Published in Pearson Frederick, Map Projections:, 2018

The differential geometry of curves is discussed to introduce needed concepts, such as radius of curvature and torsion of a space curve. The differential geometry of surfaces discussion introduces the first and second fundamental forms, as well as parametric curves and the condition of orthogonality. The surfaces of interest in mapping are surfaces of revolution. The general surface is particularized to surfaces of revolution. The process of transformation from nondevelopable to developable surfaces is considered. Representations of arc length, angles, and area, as well as the definition of the normal to the surface, are also discussed.

Berry phase of the linearly polarized light wave along an optical fiber and its electromagnetic curves via quasi adapted frame

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Journal Information

Published in Waves in Random and Complex Media, 2022

Talat Körpinar, Rıdvan Cem Demirkol

Finally, we mostly use basic mathematical operations to define and characterize the physical concepts along the manuscript, however, some degree of familiarity with differential geometry of curves and linear and vector algebra is necessary for a complete comprehension of the paper.

Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D semi-Riemannian manifold

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Journal Information

Published in Journal of Modern Optics, 2019

T. Korpinar, R. C. Demirkol

Along the manuscript, we mostly use basic mathematical operations to define and characterize the physical concepts, however, some degree of familiarity with differential geometry of curves and linear and vector algebra is necessary for a complete comprehension of the paper.

Differential geometry of curves

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Chapter 2

Berry phase of the linearly polarized light wave along an optical fiber and its electromagnetic curves via quasi adapted frame

Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D semi-Riemannian manifold