1,210 research outputs found
The Geometry and Topology on Grassmann Manifolds
This paper shows that the Grassmann Manifolds can all be
imbedded in an Euclidean space naturally and the imbedding can
be realized by the eigenfunctions of Laplacian on .
They are all minimal submanifolds in some spheres of
respectively. Using these imbeddings, we construct some degenerate Morse
functions on Grassmann Manifolds, show that the homology of the complex and
quaternion Grassmann Manifolds can be computed easily.Comment: 15 page
A Note on Characteristic Classes
This paper studies the relationship between the sections and the Chern or
Pontrjagin classes of a vector bundle by the theory of connection. Our results
are natural generalizations of the Gauss-Bonnet Theorem.Comment: 10 page
A Note on the Degenerate Morse Inequalities
In this paper we give an analytic proof of the degenerate Morse inequalities in the spirit of E. Witten. The max-min methods are used to estimate the number of ‘small’ eigenvalues of Witten’s deformed Laplacian.</p
Geometry on Grassmann Manifolds G(2,8) and G(3,8)
In this paper, we use the Clifford algebra Cℓ8 to construct fibre bundles ¿1 : G(2; 8) → S6, ¿'1 : G(2; 7) → S6 and ¿2 : G(3; 8) → S7, the fibres are CP3, CP2 and ASSOC = G2=SO(4) respectively. We show that G(2; 5), CP3 and S6 are the homologically volume minimizing submanifolds of G(2; 8) by calibrations and they generate the homology group H6(G(2; 8)). The submanifolds S7 and ASSOC of G(3; 8) generate H7(G(3; 8)) and H8(G(3; 8)) respectively.</p
- …