On variations of arclength with Myers’s and Hawking’s theorems in Riemannian and Lorentzian geometry
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Journal Title
Journal ISSN
Volume Title
School of Science |
S harjoitus- ja seminaarityöt
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Author
Date
2018
Major/Subject
Mcode
Degree programme
Language
en
Pages
35
Series
Abstract
We work through the first and second variations of arclength and discuss the rise of index forms and Jacobi fields along with their application in finding conjugate or focal points on Riemannian or Lorentzian manifolds. We then prove two theorems on the maximal distances of two conjugate or focal points along geodesics for manifolds that satisfy certain boundedness conditions for the Ricci tensor. These are Myers’s theorem in Riemannian geometry and Hawking’s theorem in Lorentzian geometry.Description
Keywords
variation, arclength, Myers's theorem, Hawking's theorem, Pseudo-Riemannian geometry, spacetime, general relativity
Other note
Citation
Mäkelä, Toni. 2018. On variations of arclength with Myers’s and Hawking’s theorems in Riemannian and Lorentzian geometry. 35.
