We use Chern–Weil theory for Hermitian holomorphic vector bundles with canonical connections for explicit computation of the Chern forms of trivial bundles with special non-diagonal Hermitian metrics. We prove that every ∂̄∂-exact real form of the type (k, k) on an n-dimensional complexmanifold X arises as a difference of the Chern character forms of trivial Hermitian vector bundles with canonic...

Many bucephalid species, mainly of the subfamily Prosorhynchinae, have been described from epinepheline serranids (groupers) throughout the World's Oceans. In this paper eight named prosorhynchine species are described and/or illustrated from epinepheline fishes from New Caledonia. Neidhartia lochepintade n. sp. in Epinephelus chlorostigma differs from other Neidhartia spp. in various combinati...

Using different forms of the arithmetic Riemann-Roch theorem and the computations of Bott-Chern secondary classes, we compute the analytic torsion and the height of Hirzebruch surfaces. 1

3 Morse-Bott theory 30 3.1 Framed moduli space . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Gradient flow lines . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Relative Morse Index . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4 Decay estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5 Transversality of M(Oa, Ob) . . . . . . . . . . . . . . . ...

These are the notes of the course given in Autumn 2007. Two good books (among many): Adams: Lectures on Lie groups (U. Chicago Press) Fulton and Harris: Representation Theory (Springer) Also various writings of Atiyah, Segal , Bott, Guillemin and Sternberg . . . .

We derive the 2-component Camassa–Holm equation and corresponding N = 1 super generalization as geodesic flows with respect to the H metric on the extended Bott-Virasoro and superconformal groups, respectively. Mathematics Subject Classifications (2000): 53A07, 53B50.

Abstract. Let G be a Banach Lie group modeled on the Banach space, possibly infinite dimensional, E. In this paper first we introduce Euler-Lagrange equations on the Lie group G with potential and right invariant metric. Euler-Lagrange equations are natural extensions of the geodesic equations on manifolds and Lie groups. In the second part, we study the geometry of the mechanical system of a r...

We investigate families of minimal rational curves on Schubert varieties, their Bott–Samelson desingularizations, and generalizations constructed by Nicolas Perrin in the minuscule case. In particular, we describe small resolutions varieties.

We compute the K-theory of complex projective spaces. There are three major ingredients: the exact sequence of K-groups, the theory of Chern character and the Bott Periodicity Theorem.

The Virasoro-Bott group endowed with the right-invariant L2metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesic distance.