differential geometry w notes from teacher_Part_73

differential geometry w notes from teacher_Part_73 - 6.1....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6.1. AFFINE CONNECTION 145 Then, if X = X i e i is a vector field, then X = X i i . If Y = Y j e j is another vector field then X Y = X i n e i ( Y k ) + k ji Y j o e k = nh dY k + k ji Y j i i ( X ) o e k . That is, X Y = X i ( i Y ) k e k where ( i Y ) k = e i ( Y k ) + k ji Y j We will often write simply i Y k meaning ( e i Y ) k . This should not be con- fused with the covariant derivative of the scalar functions Y k . The tensor field Y of type (1 , 1) with components i Y k , that is, Y = i i Y = i Y k i e k . is called the covariant derivative of the vector field Y . The components of the covariant derivative are also denoted by Y k ; i , in con- trast to partial derivatives i Y k , which are also denoted by Y k , i . In the coordinate frame e i = i the covariant derivative takes the form i Y k = i Y k + k ji Y j ....
View Full Document

This note was uploaded on 11/26/2011 for the course MAT 4821 taught by Professor Wong during the Spring '10 term at FSU.

Page1 / 2

differential geometry w notes from teacher_Part_73 - 6.1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online