লক্ষ্য করুন: এই এন্ট্রির অনুবাদ বর্তমানে মান পর্যালোচনার অধীনে রয়েছে, তাই কিছু বিষয়বস্তু সাময়িকভাবে শুধুমাত্র ইংরেজিতে প্রদর্শিত হচ্ছে।
এই এন্ট্রিটি এখনও আপনার ভাষায় অনুবাদ করা হয়নি, তাই নিচে মূল লেখাটি দেখানো হচ্ছে।
submanifold
This term is used exclusively within the specialized register of differential geometry and topology. It describes a specific relationship where a smaller geometric space is nested within a larger one while maintaining the same structural properties, such as smoothness or continuity. It is a technical term of art and is virtually never encountered in general conversation or non-mathematical writing.
In a mathematical context, the term implies a rigorous inheritance of properties from the ambient manifold. While a subset might be any collection of points, a submanifold must satisfy strict local conditions to ensure it behaves like a manifold in its own right, distinguishing it from arbitrary subsets or singular spaces.
Meanings
Examples
The sphere is a two dimensional submanifold of three dimensional Euclidean space.
The sphere is a two dimensional submanifold of three dimensional Euclidean space.
Is this particular subset actually a smooth submanifold?
Is this particular subset actually a smooth submanifold?
I need to determine if the image of this map is an embedded submanifold.
The intersection of two transverse submanifolds is also a submanifold.
The intersection of two transverse submanifolds is also a submanifold.
Wait, the boundary of the manifold is itself a submanifold of one lower dimension.
He wondered if the critical points formed a closed submanifold.
We can define a Riemannian metric on the submanifold by restricting the metric of the ambient space.
We can define a Riemannian metric on the submanifold by restricting the metric of the ambient space.
Let us assume that M is a compact submanifold of R n.