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 )
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
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
)
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