• Source: Taut submanifold

In mathematics, a (compact) taut submanifold N of a space form M is a compact submanifold with the property that for every



q
∈
M


{\displaystyle q\in M}

the distance function





L

q


:
N
→

R

,


L

q


(
x
)
=
dist
⁡
(
x
,
q

)

2




{\displaystyle L_{q}:N\to \mathbf {R} ,\qquad L_{q}(x)=\operatorname {dist} (x,q)^{2}}


is a perfect Morse function.
If N is not compact, one needs to consider the restriction of the




L

q




{\displaystyle L_{q}}

to any of their sublevel sets.




References


Kuiper, N.H. (2001) [1994], "Tight and taut immersions", Encyclopedia of Mathematics, EMS Press

Kata Kunci Pencarian:

• Teorema dasar kalkulus
• Geodesik
• Taut submanifold
• List of differential geometry topics
• Veronese map
• Nicolaas Kuiper
• Foliation
• 3-manifold
• Harmonic function