hypersphere

is likely misspelled.

has no English definition.

As a noun hypersphere

is the set of all points in a given hyperspace that are at a given distance from a given point.

In geometry|lang=en terms the difference between hypersphere and glome

is that hypersphere is (geometry) the set of all points in a given hyperspace that are at a given distance from a given point while glome is (geometry) a hypersphere in 4-dimensional euclidean space defined as the set of all points that are at a given distance from a given point, also called a 3-sphere.

As nouns the difference between hypersphere and glome

is that hypersphere is (geometry) the set of all points in a given hyperspace that are at a given distance from a given point while glome is (anatomy) one of the two prominences at the posterior extremity of the frog of a horse's foot or glome can be (obsolete) gloom.

As a verb glome is

(obsolete) to look gloomy, morose, or sullen.