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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
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
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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