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Hermitian Geometry of Twistor Spaces

Thesis Info

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Author

Danish Ali

Supervisor

Oleg Mushkarov

Program

PhD

Country

Pakistan

Thesis Completing Year

2009

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2466/1/2557S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726368844

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In the present thesis we investigate the almost Hermitian geometry of the twistor spaces of oriented Riemannian 4-manifolds. Holomorphic and orthogonal bisectional curvatures have been intensively explored on K ̈hler manifolds and a lot of important results have been obtained in this case. a But in the non-K ̈hler case these curvatures are not very well studied and it seems a that the main reason for that is the lack of interesting examples. The first part of the thesis is devoted to the study of the curvature properties of Atiyah-Hitchin- Singer and Eells-Salamon almost Hermitian structures. This is used to provide some interesting examples of almost Hermitian 6-manifolds of constant or strictly positive holomorphic, Hermitian and orthogonal bisectional curvatures. In the second part of the thesis we determine the Gray-Hervella classes of the so-called compatible almost Hermitian structures on the twistor spaces, recently in- troduced by G. Deschamps . The interest in determining these classes is motivated by the fact that the Gray-Hervella classification is a very useful tool in studying almost complex manifolds. Our results in this direction generalize the well known integrabil- ity theorems by Atiyah-Hitchin-Singer, Eells-Salamon and Deschamps and show that there is a close relation between the properties of the spectrum of the anti-self-dual Weyl tensor of an almost K ̈hler 4-manifold and the almost Hermitian geometry of a its twistor space.
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یہودیت، عیسائیت اور اسلام میں بحری حیوانات، پرندوں اور حشرات کے احکام حلت وحرمت کا تقابلی جائزہ

Almighty Allah does not leave a person free that he do what he wants like animals, but Almighty Allah made some rules for human which must be followed and obeyed by the man. In the same way some rules are declared for eating and gives permission for eating ╓alal and forbid ╓aram. No one religious in the world permission its followers to eat everything whether it is a Divine religious or non-Divine. Things which are useful for human are declared as ╒alal and things which are harmful are declared as ╒aram whether those things are related to sea food, birds, animals, insects or anything else. In this article, it is tried to compare the rules for the ╓ilat- o- ╓urmat of these things and to describe the similarity and differences of three main religions Islam, Christianity and Judaism

Cultivar Resistance and Chemical Control of Tomato Fruitworm, Heliothis Hb. Armigera on Tomato Lycopersicon Esculentum Mill.

During present investigation experiments were conducted on the pest phenology on tomato crop for three years (1989-91), at Pes t Peshawar. Institute, Tarnab, Research Agricultural pehnological studies comprised egg, larval population dynamics, spatial distribution analysis and development of larval time sequential sampling plan. On population dynamics, the regression equation for egg and/or larval population development showed feeble negative p values during 1989 and 1991, and positive p values All equations showed poor correlation during the year 1990. coefficient. The sequent ional sampling programme data showed two distinct population configurations i.e. outbreak and endemic. The differences in growth rates between types were small at first. , A total of ca . 6 samples reached to its peak and then declined. (each week) would be adequate to detect type of configuration in any one year. Spatial pattern of H. armigera Hb . egg distribution during the study revealed that index of dispersion (I.D.) values were more than 1 in 1990 and 1991. However, in 1989 the l.D. values oscillated around 1. Moreover, most of the green''s index (G.I.) values were positive which confirm the negative binomial The I.D. values of the distribution of Hÿ_ armigera Hb. eggs. spatial pattern of H. armigera Hb. larval distribution were mostly higher than 1. Therefore, larval distribution also fits negative binomial distribution. The results of discriminating doses of potassium fertilizer on egg and larval population, and the fruit infestation showed that there was no significant effect of fertilizer on the uptake of tomato plants, on egg and larval population, and on the infestation of tomato. To compare relative efficacy of nine insecticides, one application was done during the year (1989), and three during each remaining two years of study i.e. 1990 and 1991. All the insecticides were found successful in keeping the larval population below outbreak configuration level upto 15 days after spray. ( viii ) S ! Consolidation of study data over a period of three years revealed that Thiodon was statistically the most effective wiLh 77.88 percent larval mortality, followed by Folidol M (75.96%), Sevin (69.32%), Thuricide (67.12%), Dimilin (66.38%), Edcidin (65.32%) and Atabron (59.85%). Permasect and Azodrin were significantly the mortality larval and 54.66% 58.55% with effective least level). The resulLs also respectively (cdii = 17.03 at 0.05 indicated a tendency in the reduction of effectiveness of Folidol M, Azodrin, Dimilin and Thuricide over a period of three years which might probably be due to enhancement in the degree of tolerance developing in H. armiqera Hb . Cluster analysis on the interactions of eggs and larval per plant, percent fruit damage and yield in Kg per plant of 65 toniaLo cultivars gave five cluster groups. Frequency-wise cluster analysis showed two varieties in group A (3.08%), two in B (3.08%), one in C (1.53%), fifty nine in D (90.78%) and one in E (1.53%). In the regression analysis of correlation between characteristics of 65 varieties and H- armiqera Hb. infestation, step-wise model was fitted, the correlation between infestion gave negative dependence larval infestation (-0.3251) with poor correlation (-0.2558) . Similar coefficient results were obtained for correlation between yield and number of larvae per plant (b=0.4Q04, r=0 . 0893 ) The step-wise model correlation between larval chemical/physical population and parameters gave negative dependence on trichome length (-0.0100) and iron content (-15494E- 04) and positive dependence on zinc (0.0028) and vitamin C (0.0279). Cluster analysis on the interaction of larval duration, pupal duration, adult longevity, duration of life cycle, larval and pupal weight and survival to adult stage also gave five cluster groups . Frequency-wise cluster analysis showed two varieties in group A (3.08%), four in B (6.15%), fifty two in C (84.62%), three in D (4.62%) and one in E (1.53%). Tiny Tim being moderately resistant cultivar, was placed in group E. . The results indicated that integration of resistant cultivar, Tiny Tim and Bacillus thurinqiensis had maximum effect on larval mortality and minimum percent fruit infestation, it was followed by accession 87-11(1) also a resistant line, while the maximum infestation was recorded on the most susceptible cultivar, Big long. The host range and average number of larvae/plant of H. armiqera Hb were recorded on soybean (1.63), gram (4.80), tomato (0.31), tobacco (1.64), maize (0.81), sunflower (0.07), okra (0.67), potato (1.92) and burseem (0.90). Gram was observed to be the most favourable host plant of this pest