Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Fermat Metrics
View through CrossRef
In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.
Title: Fermat Metrics
Description:
In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes.
A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect.
Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used.
Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime.
Finally some possible applications to other class of spacetimes are considered.
Related Results
Fermat's Last Theorem: A Proof by Contradiction
Fermat's Last Theorem: A Proof by Contradiction
In this paper I offer an algebraic proof by contradiction of Fermat’s Last Theorem. Using an alternative to the standard binomial expansion, (a+b) n = a n + b Pn i=1 a n−i (a + b) ...
Fermat Polynomials and Extended Fermat’s Theorem
Fermat Polynomials and Extended Fermat’s Theorem
This study discusses the connection between Fermat perfect natural vectors and some specific Fermat polynomials, whose maximal root is a natural number forming part of the Fermat v...
Arithmetic properties of non-hyperelliptic genus 3 curves
Arithmetic properties of non-hyperelliptic genus 3 curves
This thesis explores the explicit computation of twists of curves. We develope an algorithm for computing the twists of a given curve assuming that its automorphism group is known....
THE SECURITY AND PRIVACY MEASURING SYSTEM FOR THE INTERNET OF THINGS DEVICES
THE SECURITY AND PRIVACY MEASURING SYSTEM FOR THE INTERNET OF THINGS DEVICES
The purpose of the article: elimination of the gap in existing need in the set of clear and objective security and privacy metrics for the IoT devices users and manufacturers and a...
Corporate environmental reporting: what's in a metric?
Corporate environmental reporting: what's in a metric?
AbstractAlthough there has been increased attention to corporate environmental reports (CERs), there has yet to be a close examination of the metrics used in these reports. Metrics...
A Note on the Beal Conjecture
A Note on the Beal Conjecture
Around $1637$, Pierre de Fermat famously scribbled, and claimed to have a proof for, his statement that equation $a^{n} + b^{n} = c^{n}$ has no positive integer solutions for expon...
A Note on the Beal Conjecture
A Note on the Beal Conjecture
Around $1637$, Pierre de Fermat famously scribbled, and claimed to have a proof for, his statement that equation $a^{n} + b^{n} = c^{n}$ has no positive integer solutions for expon...
AVERAGE FERMAT DISTANCES ON VICSEK NETWORKS
AVERAGE FERMAT DISTANCES ON VICSEK NETWORKS
The Fermat point of a triangle is a point that the total distance from the three vertices of the triangle to the point is the minimum possible. Considering the Fermat problem withi...