Riemaniann metric problem in K&N's book.
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I'm reading this book by S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry, Vol.1" and I have a problem in the proof of this lemma at the page 170:
And the proof gose like this:
My problem is that I don't understand why we can assume the last double inequality. My only idea is to look at $g$ in normal coordinates and thus $g_{ij}(x)=delta_{ij}-frac{1}{3}R_{iajb}x^ax^b+O(epsilon^3).$ Can someone help me with some details please?
riemannian-geometry inner-product-space
asked Nov 18 at 16:51
Hurjui Ionut
458211
add a comment |
up vote
3
down vote
favorite
I'm reading this book by S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry, Vol.1" and I have a problem in the proof of this lemma at the page 170:
And the proof gose like this:
My problem is that I don't understand why we can assume the last double inequality. My only idea is to look at $g$ in normal coordinates and thus $g_{ij}(x)=delta_{ij}-frac{1}{3}R_{iajb}x^ax^b+O(epsilon^3).$ Can someone help me with some details please?
riemannian-geometry inner-product-space
asked Nov 18 at 16:51
Hurjui Ionut
458211
Do you think everbody knows who K&N is?
– Paul Frost
Nov 18 at 22:57
You are right but it's a classic book.
– Hurjui Ionut
Nov 19 at 8:23
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I'm reading this book by S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry, Vol.1" and I have a problem in the proof of this lemma at the page 170:
And the proof gose like this:
My problem is that I don't understand why we can assume the last double inequality. My only idea is to look at $g$ in normal coordinates and thus $g_{ij}(x)=delta_{ij}-frac{1}{3}R_{iajb}x^ax^b+O(epsilon^3).$ Can someone help me with some details please?
riemannian-geometry inner-product-space
asked Nov 18 at 16:51
Hurjui Ionut
458211
I'm reading this book by S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry, Vol.1" and I have a problem in the proof of this lemma at the page 170:
And the proof gose like this:
My problem is that I don't understand why we can assume the last double inequality. My only idea is to look at $g$ in normal coordinates and thus $g_{ij}(x)=delta_{ij}-frac{1}{3}R_{iajb}x^ax^b+O(epsilon^3).$ Can someone help me with some details please?
riemannian-geometry inner-product-space
riemannian-geometry inner-product-space
asked Nov 18 at 16:51
Hurjui Ionut
458211
asked Nov 18 at 16:51
Hurjui Ionut
458211
edited Nov 19 at 8:24
asked Nov 18 at 16:51
Hurjui Ionut
458211
asked Nov 18 at 16:51
Hurjui Ionut
458211
asked Nov 18 at 16:51
Hurjui Ionut
458211
458211
Do you think everbody knows who K&N is?
– Paul Frost
Nov 18 at 22:57
You are right but it's a classic book.
– Hurjui Ionut
Nov 19 at 8:23
add a comment |
Do you think everbody knows who K&N is?
– Paul Frost
Nov 18 at 22:57
You are right but it's a classic book.
– Hurjui Ionut
Nov 19 at 8:23
Do you think everbody knows who K&N is?
– Paul Frost
Nov 18 at 22:57
Do you think everbody knows who K&N is?
– Paul Frost
Nov 18 at 22:57
You are right but it's a classic book.
– Hurjui Ionut
Nov 19 at 8:23
You are right but it's a classic book.
– Hurjui Ionut
Nov 19 at 8:23
add a comment |
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Do you think everbody knows who K&N is?
– Paul Frost
Nov 18 at 22:57
You are right but it's a classic book.
– Hurjui Ionut
Nov 19 at 8:23