MathDB

In 3-dimensional hyperbolic space, we are given a plane

P

and four distinct straight lines: the lines

a_1

and

a_2

are perpendicular to

P

; while the lines

r_1

and

r_2

do not intersect

P

, and their distances from

P

are equal. Denote by

S_i

the surface of revolution obtained by rotating

r_i

around

a_i

. Show that the common points of

S_1

and

S_2

can be covered by two planes.

Problem Statement