By William M. Boothby

ISBN-10: 0121160513

ISBN-13: 9780121160517

Nice introductory differential geometry textual content! I used this e-book to aid me cross my qualifying examination. Yay Boothby!

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Read or Download An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) PDF

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Extra info for An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics)

Example text

Find the locus of points such that the sum of distances from these points to the given planes is constant. 279. Given a triangle ABC. On the straight line perpendicular to the plane ABC and passing through A an arbitrary point D is taken. Find the locus of points of intersection of the altitudes of triangles DBC. 280. Given three intersecting planes and a straight line l. Drawn through a point M in space is a line parallel to l and piercing the given planes at points A, B, and C. Find the locus of points M such that the sum I AM I I BM I I CM I is constant.

Circumscribed about a ball is a frustum of a cone. The total surface area of this cone is S. Another sphere touches the lateral surface of the cone along the circle of the base of the cone. Find the volume of the frustum of a cone if it is known that the portion of the surface of the second ball contained inside the first ball has an area Q. 128. Circumscribed about a ball is a frustum of a cone whose bases are the great circles of two other balls. Determine the total surface area of the frustum of a cone if the sum of the surface areas of the three balls is equal to S.

Given a cube ABCDA 1B 1C1D 1 • Passed through the vertex A is a plane touching the sphere inscribed in the cube. Let M and N be the points of intersection of this plane and tho lines A 1B and A 1D. Prove that the line MN is tangent to the ball inscribed in the cube. 203. Prove that for a tetrahedron in which all the plane angles at one of its vertex are right angles the following statement holds true: the sum of the squared areas of rectangular faces is equal to the squared area of the fourth face (Pythagorean theorem for a rectangular tetrahedron).

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An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) by William M. Boothby


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