Consider a metric in a D-dimensional space. Simplify the following expressions, i.e. the result may be a function of D, a simple tensor that you should identify, or even a vanishing one. a) g µνgνρ b) g µνgµν c) (V µV ν − g µν V 2 )Vν d) g µν(AµBν − BµAν) e) g µνg αβ(AµBν − gµσgνρAρBσ )

Consider a metric in a D-dimensional space. Simplify the following expressions, i.e. the result may be a function of D, a simple tensor that you should identify, or even a vanishing one. a) g µνgνρ b) g µνgµν c) (V µV ν − g µν V 2 )Vν d) g µν(AµBν − BµAν) e) g µνg αβ(AµBν − gµσgνρAρBσ )

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.1: Rectangular Coordinate Systems

Problem 22E

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