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۴۹۔ قید

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الشيخ محمود بن بكر البخاري الكلاباذي: حياته وآثاره دراسة متخصّصة لكتابه ضوء السراج في علم الفرائض

Ashaykh Mahmūd bin Abī Bakr bin Abīulala bin Alī Al-bukhārī Al-kalābādhī is one of scholars of  Mirāth. He was born in 644 A.H. And died in 700 A.H. He was a man of eminence in Central Asia. He visited many metropolitan cities across the world to get knowledge. During his foreign visits, he contacted great scholars of Islamic sciences. Similarly, thousands of students used to attend his lectures. Allāmah Kalābādhī was a man of letters. He wrote many books. Famous of them are: Ḥall ul Frāi Fī Sharah Naẓm Assirājiyah, Ḍaw us Sirāj Fī Sharah Assirājiyah, Mushtabeh un Nasab Fī Asmā ur Rijāl, Mujamush Shuyūkh, Al Minhāj Al Muntakhab.

Compact Homogeneous 7-Manifolds Admitting Invariant G2 or ~ G2 -Structures

The main result of this thesis is a classification of all homogeneous spaces G/H admitting a G-invariant G2 -structure, assuming that G is a connected compact Lie group and G acts effectively on G/H. They include a subclass of all homogeneous ̃ spaces G/H with a G-invariant G2 -structure, where G is a compact Lie group. There are many new examples with nontrivial fundamental group. A formula computing the ̃ dimension of the space of G-invariant structures (resp. of G-invariant G2 -structures) on G/H is given. We study a subclass of homogeneous spaces of high rigidity and low rigidity and show that they admit families of invariant co-closed G2 -structures (resp. ̃ ̃ G2 -structures). Some new interesting examples of G2 -structures on these spaces are ̃ found. We also present a scheme of classification of G2 -structures using their intrinsic torsion.
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