2,292 research outputs found
Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics
We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic
flows admit nontrivial integrals quadratic in momenta. As an application, we
solve the Beltrami problem on closed surfaces, prove the nonexistence of
quadratically-superintegrable metrics of nonconstant curvature on closed
surfaces, and prove the two-dimensional pseudo-Riemannian version of the
projective Obata conjecture.Comment: 33 pages, 7 pictures. This paper replaces arXiv:0911.3521v1 and
arXiv:1002.013
There exist no locally symmetric Finsler spaces of positive or negative flag curvature
We show that the results of Foulon (1997 an 2002) and Kim (2007)
(independently, Deng and Hou (2007)) about the nonexistence of locally
symmetric Finsler metrics of positive or negative flag curvature are in fact
local
Closed manifolds admitting metrics with the same geodesics
The goal of this survey is to give a list of resent results about topology of
manifolds admitting different metrics with the same geodesics. We emphasize the
role of the theory of integrable systems in obtaining these results.Comment: Submitted to Conference Proceedings SPT2004: Symmetry and
perturbation theory (Cala Gonone
Comment: Food web interactions and biomanipulation in Australian reservoirs
The authors have been studying the control of phytoplankton biomass in several Australian reservoirs. To manipulate fish communities in order to reduce phytoplankton biomass, one needs a thorough understanding of processes in the plankton-associated food webs. In contrast to the situation found in lakes of the northern hemisphere, the planktivorous fish of Australian reservoirs are relatively small and they may deplete small rather than large zooplankters, so that animals as large as the adults of Daphnia carinata may avoid predation. This would result in promotion of Daphnia, particularly if fish eliminate its smaller competitors. The aim of biomanipulation should be the establishment and maintenance of a proper ratio of planktivores/piscivores, adequate for water quality requirements. Successful selection of the appropriate ratio for a given reservoir will depend on the extent of our understanding of its food web interactions. For practical application of biomanipulation in management, further development of the food web theory under Australian conditions is needed
Competetive exclusion in Cladocera through elevated mortality of adults
The population dynamics of two cladocerans, Ceriodaphnia pulchella and Diaphanosoma brachyurum competing under laboratory conditions in lake water was analysed using crosscorrelations. Both mixed and isolated populations of the two cladocerans showed delayed density dependence in the death rates of juveniles and adults as well as in fecundity rate. The regressions for each of the three rates on total density of competitors were compared between the two species. There were no significant differences in the slopes of regressions for fecundity rates and the death rates of juveniles. However, in the inferior competitor (Diaphanosoma) which went extinct in all treatments, the death rate of adults increased with total density much more quickly than in the superior competitor (Ceriodaphnia). The intraspecific comparisons indicated that while Ceriodaphnia adults survived better than juveniles under conditions of crowding, in Diaphanosoma, juveniles were better survivors than adults. These data suggest that the contention of higher vulnerability of cladoceran juveniles than adults to starvation and crowding may prove to be not a universal phenomenon
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