The geometry of symplectic pairs

We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build contact-symplectic and contact pairs from symplectic pairs.Comment: to appear in Transactions of the American Mathematical Societ

Contact pairs and locally conformally symplectic structures

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the contact pair is endowed with a normal metric, then the corresponding lcs form is locally conformally Kaehler, and, in fact, Vaisman. This leads to classification results for normal metric contact pairs. In complex dimension two we obtain a new proof of Belgun's classification of Vaisman manifolds under the additional assumption that the Kodaira dimension is non-negative. We also produce many examples of manifolds admitting locally conformally symplectic structures but no locally conformally Kaehler ones.Comment: 13 pages; corrected two misprints; to appear in Contemporary Mathematic

Stability theorems for symplectic and contact pairs

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the condition that its kernel hyperplane distribution have constant class in the sense of E. Cartan.Comment: to appear in International Mathematics Research Notice

Symplectic Pairs and Intrinsically Harmonic Forms

In this short note, we prove two properties of symplectic pairs on a four-manifold: firstly we prove that two transversal orientable foliations of codimension two, which are taut for the same Riemannian metric, are the characteristic foliations of a symplectic pair; secondly, we characterize intrinsically harmonic 2-forms of rank two as part of a symplectic pair

The geometry of recursion operators

We study the fields of endomorphisms intertwining pairs of symplectic structures. Using these endomorphisms we prove an analogue of Moser's theorem for simultaneous isotopies of two families of symplectic forms. We also consider the geometric structures defined by pairs and triples of symplectic forms for which the squares of the intertwining endomorphisms are plus or minus the identity. For pairs of forms we recover the notions of symplectic pairs and of holomorphic symplectic structures. For triples we recover the notion of a hypersymplectic structure, and we also find three new structures that have not been considered before. One of these is the symplectic formulation of hyper-Kaehler geometry, which turns out to be a strict generalization of the usual definition in terms of differential or Kaehler geometry.Comment: cosmetic changes only; to appear in Comm. Math. Phy

The catfish resources

widely distributed in the tropical Indo-Pacific and they constitute a regular, sometimes dominant, component of the demersal fish landhigs along the Indian Coast. Species of the genus Tachysurus contribute nearly 99% of the catfish catch, particularly T. thalassinus. T. tenuispinis, T. serratus and T. dussumieri. Osteogeneiosus militaris also forms a fishery along the northwest coast

Taxonomic considerations and general distribution of commercially important catfishes

The taxonomy of our commercially important marine catfishes is still in a state of uncertainty. The nomenclature has suffered a lot of changes brought about by various taxonomists. When some authors have used the genus name Tachysurus, and hence the family name Tachysuridae, others preferred the name Anus and the family name Ariidae. Valenciennes (1840), Bleeker(1847), Gunther (1864), Day (1878), Weber and Beaufort (1913), Herre (1953), Jordan (1963), Fischer and Whithead (1974) and Fischer and Bianchi (1984) all have used the name >4r/us Val. 1840, whereas Fowler (1941), Chandy (1953), Munro (1955), Tilak (1965), Jayaram and Dhanze (1978 a, 1978 b) and Menon (1979) replaced the name Ar/us Val. 1840 by Tachysurus Lacepede 1803