Beginner's book for Riemannian geometry

Question

Could you recommend some beginner books for Riemannian geometry to me?

I am completely new to Riemannian geometry, but have some basic knowledge of differential geometry.

I am looking for a book in Riemannian which is similarly as light as Tu's "Introduction to Manifolds" for differential geometry. I know that the classical reference is the book of do Carmo, but I have heard some students complaining that its not a book for the absolute beginner.

For the moment, I am just looking for a source to introduce me Riemannian metrics, Riemannian manifolds, curvature, geodesics in a way as clear as possible.

Thank you

Do Carmo's book "Riemannian Geometry" is a nice introductory book. — Andre of Astora, Nov 11 '19 at 20:24

Michael Albanese · Accepted Answer · 2018-04-11T11:08:26.573

I'm a fan of Lee's Riemannian Manifolds: An Introduction to Curvature. It is definitely an introductory book; there are many deeper topics that it doesn't mention (compare to Peterson's Riemannian Geometry). Here is an excerpt from the preface:

"I have selected a set of topics that can reasonably be covered in ten to fifteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject."

One of the features that I really like about this book is the careful treatment of tensors and tensor fields (chapter 2). Understanding exactly what these objects are is one of the potential obstructions to learning Riemannian geometry.

Btw, there is a new edition for this book. See here. Definitely better than the first edition. — Kelvin Lois, Apr 02 '19 at 05:04

score 7 · Answer 2 · answered Apr 11 '18 at 12:54

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Actually there is a book by Tu himself about Riemannian geometry. It was just released last year. It is called Differential Geometry - Connections, Curvature and Characteristic Classes and is published by Springer.

answered Apr 11 '18 at 12:54

TheGeekGreek

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score 6 · Answer 3 · answered Nov 25 '15 at 16:14

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By far Gallot et al is a very good choice.

answered Nov 25 '15 at 16:14

janmarqz

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also relevant http://math.stackexchange.com/questions/284185/good-problem-book-in-differential-geometry to see – janmarqz Nov 25 '15 at 16:53
and more on topic http://math.stackexchange.com/questions/1460031/introductory-book-for-riemannian-geometry?rq=1 – janmarqz Nov 25 '15 at 16:54
an another http://math.stackexchange.com/questions/765972/prerequisite-for-petersens-riemannian-geometry?rq=1 – janmarqz Nov 25 '15 at 16:55

score 5 · Answer 4 · answered Nov 25 '15 at 16:18

5

Have you tried Riemannian Geometry: A Beginners Guide, by Frank Morgan?

answered Nov 25 '15 at 16:18

Franciele Daltoé

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score 3 · Answer 5 · answered Nov 25 '15 at 17:01

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Milnor "Morse Theory" contains an extremely well written introduction to the subject.

answered Nov 25 '15 at 17:01

Thomas

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score 2 · Answer 6 · edited Mar 20 '19 at 03:40

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Riemannian Geometry by S.Gallot, D.Hulin, J.Lafontaine is a great book which contains a lot more than one could learn in an introductory course in Riemannian geometry. I would suggest this book if you already have some idea in the subject. Reading this book for someone new to the subject might be cumbersome and intimidating.

Have fun :)

edited Mar 20 '19 at 03:40

Xander Henderson

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answered Mar 20 '19 at 03:21

GAUTAM NEELAKANTAN

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score 2 · Answer 7 · edited Nov 11 '19 at 16:34

2

Differential Geometry of Manifolds by U.C De and A.A Shaikh is also good book for beginners.

All concepts in this book are given in detail and it's good if you want to go through all concepts.

edited Nov 11 '19 at 16:34

Ertxiem - reinstate Monica

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answered Nov 11 '19 at 15:44

sweety tarika

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Beginner's book for Riemannian geometry

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