For any positive number k, an immersion z: MC² defined by x(u, v) = (u, k cos v, v, k sin v). Then: (i) Show that M is a slant surface in C². (ii) Find the slant angle of A1. (iii) Find the second fundamental form corresponding to each vector field i.e., h(e,, ej), 1≤ i, j≤ 2.
For any positive number k, an immersion z: MC² defined by x(u, v) = (u, k cos v, v, k sin v). Then: (i) Show that M is a slant surface in C². (ii) Find the slant angle of A1. (iii) Find the second fundamental form corresponding to each vector field i.e., h(e,, ej), 1≤ i, j≤ 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(iii) only in detail.
![Department of Mathematics
6. For any positive number k, an immersion z: MC² defined by
x(u, v) = (u, k cos u, v, k sin v).
Then:
(i) Show that M is a slant surface in C².
(ii) Find the slant angle of A.
(iii) Find the second fundamental form corresponding to each vector field i.e., h(e, ej), 1≤
i, j≤ 2.
(iv) Find the constant mean curvature of M.
(y) Show that M is neither totally geodesic (i.e., h 0 for at least some e,, ej, 1 ≤
i, j≤2) nor minimal (i.e., H # 0) submanifold.
CD manifold M of a Kaehler manifold](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e0160f-3c30-4d27-95cf-afb7f00ec41f%2F9aa4086b-9e96-494d-ae6e-b3d2bccfe272%2Fn454gmh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Department of Mathematics
6. For any positive number k, an immersion z: MC² defined by
x(u, v) = (u, k cos u, v, k sin v).
Then:
(i) Show that M is a slant surface in C².
(ii) Find the slant angle of A.
(iii) Find the second fundamental form corresponding to each vector field i.e., h(e, ej), 1≤
i, j≤ 2.
(iv) Find the constant mean curvature of M.
(y) Show that M is neither totally geodesic (i.e., h 0 for at least some e,, ej, 1 ≤
i, j≤2) nor minimal (i.e., H # 0) submanifold.
CD manifold M of a Kaehler manifold
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