Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science

2023-10-23

2023

Kalogeris Ioannis

Παναγιώτης Γιαννιώτης, Επίκ. Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ,
Διονύσιος Λάππας, Αναπλ. Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ,
Γεράσιμος Μπαρμπάτης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ

Exploring Obata's theorem: Insights and Applications in Differential Geometry

English

Εξερευνώντας το Θεώρημα του Obata: Ερμηνεία και Εφαρμογές στη Διαφορική Γεωμετρία

This master’s thesis delves into the intricate realm of differential geometry by comprehensively investigating Obata’s Theorem, its extensions, relations and similarities to other important theorems in Riemannian Geometry. Obata’s Theorem, a fundamental result in Riemannian geometry, establishes a profound connection between the curvature of a Riemannian manifold and the behavior of the eigenvalues of the Laplace operator under isometric deformations. Through a meticulous examination of the theorem’s origins, proofs, and implications, this research uncovers its deep-seated mathematical foundations and unveils its significance in the broader context of differential geometry. The thesis not only presents a rigorous exposition of Obata’s original proof but also explores subsequent developments that have emerged in the mathematical discourse. By elucidating the intricate interplay between curvature, isometries, and eigenvalues, this study contributes to a more profound understanding of the geometric and topological properties underlying Riemannian manifolds.

Science

Obata's theorem, differential geometry, Ricci curvature, Laplace operator

Yes

1

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16

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https://pergamos.lib.uoa.gr/uoa/dl/object/3361960