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Description
Differential GeometryThis is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables.The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a general theory of connections.
The author presents a full development of the Erlangen Program in the foundations of geometry as used by Elie Cartan as a basis of modern differential geometry; the book can serve as an introduction to the methods of E. Cartan. The theory is applied to give a complete development of affine differential geometry in two and three dimensions.
Although the text deals only with local problems (except for global problems that can be treated by methods of advanced calculus), the definitions have been formulated so as to be applicable to modern global differential geometry. The algebraic development of tensors is equally accessible to physicists and to pure mathematicians. The wealth of specific resutls and the replacement of most tensor calculations by linear algebra makes the book attractive to users of mathematics in other disciplines.
Binding Type: Paperback
Publisher: Dover Publications
Published: 06/01/1977
ISBN: 9780486634333
Pages: 400
Weight: 0.93lbs
Size: 8.24h x 5.62w x 0.77d
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★★★★★ 5
Good For Heavy Chewers So Far
Color: Onyx Black - Most Durable
Solid quality. My Doberman is a power chewer and I am looking for a toy that he can't destroy in 2 seconds. If a ball lasts more than an hour it is a miracle. It has a sturdy design and is more heavy weight than the other "non-destructible" balls he has. He has only had his ball for one day so we will see how long this ball lasts him. It is the size of a tennis ball, firm, little to no bounce, and seems built for heavy chewing.
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Reviewed in the United States on January 30, 2026
★★★★★ 5
Great Product, 2 years and running!
Color: Onyx Black - Most Durable
It’s been almost 2 years and my dogs haven’t destroyed them yet. I have a Pitbull and a Pit/Cosro mix. They destroy every toy we’ve given them, except these toys. Great product 100% worth the money
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Reviewed in the United States on March 29, 2026
★★★★★ 5
Perfect for HEAVY chewers
Color: Onyx Black - Most Durable
My dog is a heavy chewer. Destroys everything that’s not very hard rubber, hard plastic, or hard material. He LOVES this ball. I think it’s his favorite. Plus, it bounces great so you can play with your dog. Very well constructed- probably indestructible or will at least last a very long time. Easily worth the money.
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Reviewed in the United States on February 7, 2026
★★★★★ 5
The only toy my dogs can’t destroy and love
Color: Onyx Black - Most Durable
I am thrilled to have found one toy my dogs don’t destroy immediately. They have torn up Fenrir hammers, the black kongs of all sizes, the monster k9 stick, nylabones, and they don’t like the goughnut at all (it stinks like a bad tire). This is the first one they both love and haven’t been able to destroy immediately. It does allow little tooth marks, but that’s what makes it fun for them. They are very happy playing with it and I’d say this one was worth every dollar.
Update Months Later: We’ve gone through 2/3 now. I got two initially, and one has lasted long term. They still haven’t completely destroyed it. They did destroy a second one quickly so I suspect a flaw in it. They sent me a new one and they took a while, but they did destroy the third to the point we had to throw it away. Despite that, one still remains and our dogs still love it. It’s still the best for the money compared to others. We have two Bully XL’s that are each close to 100 pounds.
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Reviewed in the United States on April 11, 2024
★★★★★ 5
Indestructible
Color: Onyx Black - Most Durable
This is actually indestrutible! Be careful though, it's wicked hard/heavy. It isn't a ball you want banging into things. Use outside!!
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Reviewed in the United States on April 23, 2026