کلاسه‌بندی کلاف کروی مماس مجهز به ساختار تقریبا ب-مرتبط

نویسندگان
اسماعیل پیغان 1
فرشاد فیروزی 2
1 دانشگاه اراک
2 دانشگاه پیام نور
10.52547/mmr.7.3.467
چکیده
در ابتدا، کلاف کروی مماس بر یک منیفلد ریمانی به عنوان یک منیفلد با بعد در نظر گرفته می‌شود و در پی آن، ما این کلاف کروی را به یک متریک طبیعی به انضمام یک ساختار تقریباً ب-مرتبط تجهیز خواهیم نمود. در گام بعدی، مولفه‌های تانسور ساختاری متناظر با این کلاف کروی را محاسبه می‌کنیم. آن‌گاه، با توجه به کلاسه‌بندی ساختارهای تقریباً ب-مرتبط (که ما آن را به ایجاز، کلاسه‌بندی هم‌بسته[1] می‌نامیم)، به کلاسه‌بندی کلاف کروی مماس مجهز به ساختار تقریباً ب-مرتبط طبیعی اهتمام می‌ورزیم و کلاس‌هایی را که کلاف کروی مماس با ساختار یادشده به آن‌ها تعلق دارد، به دست می‌آوریم. هم‌چنین، ما روابطی بر حسب تانسورهای انحنا به دست می‌دهیم که با برقراری آن‌ها، کلاف کروی با ساختار مذکور می‌تواند به هر یک از این کلاس‌های یازده‌گانه تعلق داشته باشد


[1] Relevant Classification
کلیدواژه‌ها
ساختار تقریبا مرتبط
کلاف کروی
متریک طبیعی

عنوان مقاله English

On the Classifying of the Tangent Sphere Bundle with Almost Contact B-Metric Structure

نویسندگان English

Esmaeil Peyghan 1
Farshad Firuzi 2
1 Arak University
2 Payame Noor university
چکیده English

One of the classical fundamental motifs in differential geometry of manifolds is the notion of the almost contact structure. As a counterpart of the almost contact metric structure, the notion of the almost contact B-metric structure has been an interesting research field for many mathematicians in differential geometry of manifolds, and the geometry of such structures has been studied frequently. There is a classification for the almost contact B-metric structures, named the relevant classification, with respect to the covariant derivative of the fundamental tensor of type (1, 1). In this paper, we basically use this classification to achieve our goals. On the other hand, many of mathematicians have widely considered the concept of lifted metric on the tangent bundle and tangent sphere bundle of a Riemannian manifold (M, g). The idea of constructing a lifted metric on the tangent bundle was a strong inspiration for many of mathematicians and finally, the notion of g-natural metric as the most general type of lifted metrics on tangent bundle TM of a Riemannian manifold (M, g) was introduced in 2005. In this paper, we consider a pair of associated g-natural metrics on the unit tangent sphere bundle T1M with B-metric, and we classify this structure with respect to the relevant classification of almost contact manifold with B-metric.

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کلیدواژه‌ها English

almost contact structure
sphere bundle
natural metric
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