ar X iv : m at h - ph / 0 60 50 74 v 1 2 9 M ay 2 00 6 BRYANT - SALAMON ’ S G 2 - MANIFOLDS AND THE HYPERSURFACE GEOMETRY
نویسنده
چکیده
We show that two of Bryant-Salamon’s G2-manifolds have a simple topology, S \ S or S \ CP . In this connection, we show there exists a complete Ricci-flat (non-flat) metric on Sn \ Sm for some n − 1 > m. We also give many examples of special Lagrangian submanifolds of T ∗Sn with the Stenzel metric. The hypersurface geometry is essential in the argument.
منابع مشابه
ar X iv : m at h - ph / 0 60 50 74 v 2 2 J un 2 00 6 THE BRYANT - SALAMON G 2 - MANIFOLDS AND HYPERSURFACE GEOMETRY
We show that two of the Bryant-Salamon G2-manifolds have a simple topology, S \S or S \CP . In this connection, we show there exists a complete Ricci-flat (non-flat) metric on Sn \ Sm for some n − 1 > m. We also give many examples of special Lagrangian submanifolds of T ∗Sn with the Stenzel metric. Hypersurface geometry is essential for these arguments.
متن کاملar X iv : m at h / 05 05 66 9 v 1 [ m at h . D G ] 3 1 M ay 2 00 5 INVARIANT RIEMANNIAN METRICS AND f - STRUCTURES ON FLAG MANIFOLDS
It turns out that if a reductive complement m of a homogeneous reductive space G/H possesses a number of properties (including its decomposability into an orthogonal sum of three Ad(H)-invariant irreducible subspaces) then there exists a simple way of determining whether an f -structure F on this space belongs to the classes G1f , NKf and Kill f of generalized Hermitian geometry with respect to...
متن کاملar X iv : m at h - ph / 0 20 80 41 v 2 9 O ct 2 00 2 Geometry of the Triangle Equation on Two - Manifolds ∗
A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order difference “black and white triangle operators (equations)” on triangulated surfaces with a black and white coloring of triangles. In this work, we develop the theory of these operators and equations, showing their simila...
متن کاملar X iv : 0 80 1 . 08 75 v 3 [ m at h . D S ] 1 5 M ay 2 00 8 GROUPS NOT ACTING ON MANIFOLDS
In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that “generic” finitely generated groups have no smooth volume preserving actions on compact manifolds while also producing many finitely presented, torsion free groups with the same property.
متن کاملar X iv : 0 70 5 . 41 66 v 1 [ m at h . G T ] 2 9 M ay 2 00 7 CLASSIFICATION OF FRAMED LINKS IN 3 - MANIFOLDS
We present a short proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: Theorem. Let M be a connected oriented closed smooth 3-manifold. Let L1(M) be the set of framed links in M up to a framed cobordism. Let deg : L1(M) → H1(M ;Z) be the map taking a framed link to its homology class. Then for each α ∈ H1(M ;Z) there is a 1-1 ...
متن کامل