Line segments are usually straight, so they should not be curved. In the strict definition of mathematical geometry, a line segment is a finite part between two points in a straight line and is continuous, so the line segment cannot be curved. It always represents a part of a straight line, from one end to another, with no twists or curves between the two endpoints.
When we talk about line segments, it is common to default to its definition in planar geometry, which is the shortest distance between two points. This kind of line segment has two endpoints and is straight and neither bent. This is the basic definition and property of a line segment. In spherical geometry, the "shortest distance" between two points is no longer a straight line in the traditional sense, but a large arc. This great arc is straight on the spherical surface, but it is curved in a straight line as we usually understand it. So, in this case, we can say that the line segments on the sphere are curved.
In addition, in higher-dimensional geometry, the definition and properties of line segments become more complex and diverse. In high-dimensional space, the "shortest distance" between two points may no longer be a straight line in the traditional sense, but some kind of complex curve or surface.
In the field of art, curved line segments are not only accepted, but are often used to create unique effects. For example, in painting and design, curved lines are used to express movement, femininity, or breaking rules.
When we look at the world from different perspectives, we find that geometric forms are not static, but full of infinite possibilities.