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Title: Paired curves on riemannian manifolds
Researcher: Bhat, Vishesh S
Guide(s): Baskar, Hari R
University: CHRIST University
Completed Date: 26-02-2019
Abstract: The thesis examines certain curves in Riemannian manifolds, which exist in one-one correspondence with other curves. This correspondence is described by means of a rigid link between the frame vectors allied newlineto these quotpairedquot curves. The Combescure transformation is made use of to exhibit that one of the paired curves can be obtained as an infinitesimal deformation of the other. The correspondence between the paired curves is exploited to formulate expressions relating the curvature and torsion functions of one with the other. newlineThe primary setting for this study is the Euclidean space R3, with brief considerations of 3-dimensional Riemannian space forms(i.e. Riemannian manifolds of constant sectional curvature). The exponential map is the desired tool of analysis in the latter case. The major classes of curves treated are the Mannheim class of curves in R3 and their partner curves. Further, with the help of the newlinenotion of the osculating helix, a new class of curves called constantpitch curves are defined, which are seen to naturally arise in motion analysis studies in theoretical kinematics. Constant-pitch curves are newlinealso shown to be inherent counterparts of Mannheim curves by means of a deformation. newlinePivotal properties of Mannheim and constant-pitch curves are established and a few examples are put forth. Integral characterizations of both curves are derived in terms of their spherical indicatrices. A newlineconsequence of this to geometric modeling problems involving energy functionals and also to the study of elastic curves is discussed. newlineCertain ruled surfaces generated by Mannheim and constant-pitch curves which occur as axodes associated to a rigid body motion are newlinedetailed and their applications to kinematics are studied. Further, the nature of paired curves in connection with tubular neighbourhoods/surfaces are investigated. newline
Pagination: A4
Appears in Departments:Department of Mathematics and Statistics

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02_declaration.pdf202.95 kBAdobe PDFView/Open
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04_acknowledgements.pdf71.87 kBAdobe PDFView/Open
05_abstract.pdf66.68 kBAdobe PDFView/Open
06_contents.pdf70.17 kBAdobe PDFView/Open
07_list_of_figures.pdf91.08 kBAdobe PDFView/Open
08_chapter1.pdf123 kBAdobe PDFView/Open
09_chapter2.pdf238.49 kBAdobe PDFView/Open
10_chapter3.pdf357.55 kBAdobe PDFView/Open
11_chapter4.pdf314.33 kBAdobe PDFView/Open
12_chapter5.pdf279.93 kBAdobe PDFView/Open
13_chapter6.pdf398.47 kBAdobe PDFView/Open
14_chapter7.pdf78.71 kBAdobe PDFView/Open
15_bibliography.pdf105.92 kBAdobe PDFView/Open
16_publications.pdf76.05 kBAdobe PDFView/Open

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