50 50 67 v 2 2 6 M ay 2 00 5 Intersections of Lagrangian submanifolds and the Mel ’ nikov “ function ” Nicolas Roy

0 50 50 67 v 1 2 5 M ay 2 00 5 The geometry of the Mel ’ nikov “ function ”

We make explicit the geometric content of Mel’nikov’s method for detecting heteroclinic points between transversally hyperbolic periodic orbits. After developing the general theory of intersections for pairs of family of Lagrangian submanifolds constrained to live in an auxiliary family of submanifolds, we explain how the heteroclinic orbits are detected by the zeros of the Mel’nikov 1-form. Th...

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

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.

ar X iv : n uc l - th / 0 50 50 24 v 1 9 M ay 2 00 5 Structure of isomeric states in 66 As and 67 As

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.

0 50 60 66 v 2 3 M ay 2 00 6 Existence of Spontaneous Pair Creation