Moduli spaces M of self-dual SU(2) connections (“instantons”) over a compact Riemannian 4.manifold (hl, g) carry a natural L2 metric g, which is generally incomplete. For instantons of Pontryagin index 1 over a compact, simply connected, oriented, positive-definite base manifold, the completion M is Donaldson’s compactification; in fact the boundary of the completion is an isometric copy of (M,...

We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its “boundary depth,” and establish basic results about how the boundary depths of different Hamiltonians are related. As applications, we prove that certain Hamiltonian symplectomorphisms supported in displaceable subsets have infinitely many nontrivial geometrically distinct periodic ...

Let M be a compact irreducible Hermitian symmetric space and write M = G/K, with G the group of holomorphic isometries of M and K the stability group of the point of 0 ∈ M . We determine the maximal dimension of a complex projective space embedded in M as a totally geodesic submanifold. AMS Subject Classification: 14L35, 22F30, 20G05 Introduction Let M be a simply connected compact complex mani...

Abstract We extend the Polydisk Theorem for symmetric bounded domains to Cartan–Hartogs domains, and apply it prove that a domain inherits totally geodesic submanifolds from which is based on, give characterization of Cartan–Hartogs’s geodesics with linear support.

In this paper we present the first example of a primitive, totally geodesic subvariety F ⊂ Mg,n with dim(F ) > 1. The variety we consider is a surface F ⊂M1,3 defined using the projective geometry of plane cubic curves. We also obtain a new series of Teichmüller curves in M4, and new SL2(R)–invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms.

We bound the geodesic residual finiteness growths of closed hyperbolic manifolds that immerse totally geodesically in non-compact right-angled reflection orbifolds, extending work of the fourth author from the compact case. We describe a rich class of arithmetic examples to which this result applies, and apply the theorem to give effective bounds on the geodesic residual finiteness growths of m...

In this paper, first we define Clairaut Riemannian map between manifolds by using a geodesic curve on the base space and find necessary sufficient conditions for to be with nontrivial example. We also obtain condition harmonic. Thereafter, study from manifold Ricci soliton scalar curvatures of $rangeF_\ast$ $(rangeF_\ast)^\bot$ soliton. Further, leaves almost Einstein. vector field $\dot{\beta}...

In this paper, we study a stability problem of free boundary hypersurfaces, and also capillary ones whose supported on horosphere in hyperbolic space. We prove that umbilical hypersurfaces are only stable immersed horosphere. Using the same method, show totally geodesic hyperplane is type-II hypersurface

Moving our hands smoothly is essential to execute ordinary tasks, such as carrying a glass of water without spilling. Past studies [1-3] have revealed a natural tendency to generate smooth trajectories when moving the hand from one point to another in free space. Here we provide a new perspective on movement smoothness by showing that smoothness is also enforced when the hand maintains contact ...