Complete Calabi-Yau metrics from Kahler metrics inD=4

Abstract

In the present work, a family of Calabi-Yau manifolds with a local Hamiltonian Killing vector is described in terms of a non linear equation whose solutions determine the local form of the geometries. The main assumptions are that the complex (3, 0)-form is of the form e ik Ψ, where Ψ is preserved by the Killing vector, and that the space of the orbits of the Killing vector is, for fixed value of the momentum map coordinate, a complex 4-manifold, in such a way that the complex structure of the 4-manifold is part of the complex structure of the complex 3-fold. The family considered here include the ones considered in [26]-[28] as a particular case. We also present an explicit example with holonomy exactly SU(3) by use of the linearization introduced in [26], which was considered in the context of D6 branes wrapping a complex 1-cycle in a hyperkahler 2-fold.

Stridulation and Its Analysis in Certain Geocorisae (Hemiptera Heteroptera)

“…The sound output of the present insects (except Coranus) is of this pulse modulated type but it would be premature on this ground alone to postnlate the existence of auditory receptors capable of responding in a typical manner to such sounds. However, the considerable structural adaptation in, for example, P. quadrnta connected with the sound producing organs (Leston, 1957) may imply an active advantage accruing to the insect from stridulation, and it seems inconceivable that the elaborate neuromotor reflexes which have evolved in Sehirus bicolor to enable it to produce such a variety of sounds represent an accidental and useless adaptation. The fact that sound production in most of the present insects is related to the period of sexual maturity lends further weight to the theory that the sounds and the behaviour associated with them are concerned in bringing the sexes together and facilitating mating.…”

“…Stridulation was recorded on a Vortexion recorder type WVA, which had a frequency response of 50c/s-l3kc/s. Thus any ultrasonic emission by the insects was not recorded, and although from the description of the mechanisms concerned given by Leston (1957) it would appear unlikely that such high frequency sounds would be generated, nevertheless this omission should be remembered.…”

“…Kleidocerys resedae (Panzer), Kleidocerys ericae (Horvath), (Lygaeidae) Leston (1955) has suggested that each of these closely related bugs emits two calls, one probably related to courtship and the other an aggregating call leading to the formation of heterosexual groups. The former has not been recorded, but the latter has been recorded and analysed.…”

“…The first pulse is always very weak and in many oscillogram records becomes vanishingly small in relation to the noise track. The relationship between the structure and movements of the stridulatory mechanism of Sehirus (Leston, 1957) to this complex sound is not clear ; it would appear to require four separate strokes of the strigil over the plectrum to produce such distinct pulses, but this would entail extremely rapid movement of the abdominal plectrum ; the changes in intensity of the pulses have also to be explained.…”

“…The first of a series of papers on sound production in the Heteroptera deals with the mechanisms concerned in stridulation and their occurrence in different families (Leston, 1957). The present paper describes the recording of sounds made by several species of terrestrial Heteroptera, the physical analysis of these sounds, and their possible behavioural significance.…”